Why don't they just come here legally like my great-grandparents did?

Why? 1. Because it used to be a lot easier to come here "legally"; 2. Because it once was easier to legalize yourself even if you came here illegally; 3. Because it used to be easy to come back legally even if you had been here illegally in the past.

Here is some history of immigration law from the USCIS itself:

Act of March 3, 1875 (18 Statutes-at-Large 477)

Established the policy of direct federal regulation of immigration by prohibiting for the first time entry to undesirable immigrants. Provisions:


a. Excluded criminals and prostitutes from admission.

b. Prohibited the bringing of any Oriental persons without their free and voluntary consent; declared the contracting to supply “coolie” labor a felony.

c. Entrusted the inspection of immigrants to collectors of the ports.
 
Immigration Act of August 3, 1882 (22 Statutes-at-Large 214)

First general immigration law, established a system of central control of immigration through State Boards under the Secretary of the Treasury. Provisions:

a. Broadened restrictions on immigration by adding to the classes of inadmissible aliens, including persons likely to become a public charge.

b. Introduced a tax of 50 cents on each passenger brought to the United States.
 
Immigration Act of March 3, 1903 (32 Statutes-at-Large 1213)

An extensive codification of existing immigration law. Provisions:

a. Added to the list of inadmissible immigrants.

b. First measure to provide for the exclusion of aliens on the grounds of proscribed opinions by excluding “anarchists, or persons who believe in, or advocate, the overthrow by force or violence the government of the United States, or of all government, or of all forms of law, or the assassination of public officials.”

c. Extended to three years after entry the period during which an alien who was inadmissible at the time of entry could be deported.

d. Provided for the deportation of aliens who became public charges within two years after entry from causes existing prior to their landing.

e. Reaffirmed the contract labor law (see the 1885 act).

Immigration Act of May 26, 1924 (43 Statutes-at-Large 153)


The first permanent limitation on immigration, established the “national origins quota system.” In conjunction with the Immigration Act of 1917, governed American immigration policy until 1952 (see the Immigration and Nationality Act of 1952).

Provisions:

a. Contained two quota provisions:

1. In effect until June 30, 1927—set the annual quota of any quota nationality at two percent of the number of foreign-born persons of such nationality resident in the continental United States in 1890 (total quota - 164,667).

2. From July 1, 1927 (later postponed to July 1, 1929) to December 31, 1952—used the national origins quota system: the annual quota for any country or nationality had the same relation to 150,000 as the number of inhabitants in the continental United States in 1920 having that national origin had to the total number of inhabitants in the continental United States in 1920.

Preference quota status was established for: unmarried children under 21; parents; spouses of U.S. citizens aged 21 and over; and for quota immigrants aged 21 and over who are skilled in agriculture, together with their wives and dependent children under age 16.

b. Nonquota status was accorded to: wives and unmarried children under 18 of U.S. citizens; natives of Western Hemisphere countries, with their families; nonimmigrants; and certain others. Subsequent amendments eliminated certain elements of this law’s inherent discrimination against women but comprehensive elimination was not achieved until 1952 (see the Immigration and Nationality Act of 1952) 
 
c. Established the “consular control system” of immigration by mandating that no alien may be permitted entrance to the United States without an unexpired immigration visa issued by an American consular officer abroad. Thus, the State Department and the Immigration and Naturalization Service shared control of immigration.


d. Introduced the provision that, as a rule, no alien ineligible to become a citizen shall be admitted to the United States as an immigrant. This was aimed primarily at Japanese aliens.

e. Imposed fines on transportation companies who landed aliens in violation of U.S. Immigration laws.

f. Defined the term “immigrant” and designated all other alien entries into the United States as “nonimmigrant” (temporary visitor). Established classes of admission for nonimmigrant entries.
 
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RAD~
So in the old days if you showed up and you weren't a criminal or a prostitute (or sadly, Asian) you got in "legally". The US didn't even use visas until after the 1924 law. Similarly, if you were inadmissible but managed to get in you could stay anyway after the three year statute of limitations ran out.
 
In those days there were no real numerical limits on immigrants - when you decided to come to the US - you came to the US. You simply needed to be able to afford the trip and convince the inspector you would be able to support yourself.
 
Now there are seven million people waiting in line for less than 400K available visas. The waiting times are multiple decades for some categories. This doesn't even take into account the ten to twelve million people here already without legal status. Why does it surprise anyone that this system doesn't work and that some people try to go around the law? If your spouse was living in the United States legally and filed paperwork for you and the children to come live legally in the USA in six years - how would that sound? (click the title above to see the report from the National Visa Center in Portsmouth - courtesy of ILW.com)
 
In the 1990s the law changed so that people who were in the United States for one year out of status would be barred from returning legally for 10 years even if they qualified for a visa. After 2001, no new "adjustment of status" paperwork can be filed for people here in the US who entered illegally even if they have approved visa petitions from US citizen relatives and are willing to pay a $1,000.00 penalty fee.
 
So they can't stay and get legal and they can't leave to try to come back legally either. Where does that leave us as a country? With people who have no chance of getting here legally any time soon either waiting at home for years separated from their loved ones or finding an "extralegal" method of getting here and remaining here out of legal status.
 
In doing research on immigration and geneaology, I have noticed that immigrants in the 1790s - 1920s often would come here alone and spend a year or even two working and making a home before sending for the rest of the family. That was a necessary hardship that many families undertook - I cannot remember ever seeing people waiting 5 or 10 years to bring their families to the USA nevermind the 23 years currently forecast for Philippines 4th preference petitions. 
 
So the fact of the matter is...most of our immigrant ancestors would be turned away if they tried to get in here today. This system is not working and needs to be reformed. I believe immigration has historically contributed to the strength and vitality to this country. There do have to be reasonable controls on immigration - but our current system is anything but reasonable.