The problem is that as a practical matter it's not possible to "seal the border".
For example, a number of years ago they found that drug smugglers had constructed an UNDERGROUND tunnel from Mexico into Texas. It STARTED under a warehouse-type business in Mexico, was several hundred yards long, and terminated in a warehouse-type building in Texas.
And if they DID provide "easy paths", then MILLIONS of ADDITIONAL people would show up. MOST of the folks who WOULD be allowed in would tell folks back home--"Come! *I* got in--YOU can get in."
Back in 1986 with the Reagan amnesty I tried getting into immigration law. I had people come as potential clients who had been in the U.S. illegally for 15 YEARS or more. And now--FINALLY it would pay off.
The problem with ANY kind of amnesty / work visa / etc., is that that just opens the door to--"Hey--it was a LONG wait for ME, but you WILL be able to find work OFF THE BOOKS, etc. and SOMEDAY you WILL be able to LEGALLY stay here permanently."
There's also the problem that MOST of the people who would show up are NOT well educated, DON'T speak English, and DON'T have the skills to get a decent-paying job in the U.S. job market. It's not the folks who graduated from Central or South American universities, where they studied English in addition to a major in something like engineering, accounting, management, etc.
Those no-skills people would wind up COMPETING for low-level jobs with native-born Americans, who would be outraged--and would vote into office legislators who would repeal those laws.
Also, there are MILLIONS of people in other countries who DO have skills, DO meet all the qualifications to emigrate, etc., and who are "waiting their turn" to do it LEGALLY.
And now people are just SHOWING UP basically saying--"SCREW THEM!! I JUST DECIDED TO *SHOW UP* SO YOU *HAVE TO* GIVE *ME* PRIORITY--EVEN THOUGH I *DON'T* MEET *ANY* QUALIFICATIONS and have NOTHING TO OFFER!!"