Of course not, when catch and releases confers legality until some distant court date. Surely you understand most people don't use the narrow definition you rely on to undermine their legitimately felt outrage. FYI, no man on the street would agree there have only been 1,000,000 under 3.5 years of Biden when the daily numbers reported are 4,000 or 8,000, sometimes 12,000, sometimes more.

But the "man on the street" probably doesn't understand that a border "encounter" (which can hit those levels) is not nearly the same thing as an asylum request or other outcome that results in a person staying here for any length of time.

Look, it's just not possible. The entire population of the U.S. has only increased by about 4.4 million people since 2020:

en.wikipedia.org - Demographics of the United States

It's literally impossible for 10 million new people to now be residing in the country. It's impossible for there to be 4 million new people to now be residing in the country that arrived illegally and/or are pending asylum claims (because the population is growing through other means, including legal immigration).

Why the disconnect? Partially because Title 42 expulsions were running until May of 2023 - it's barely been over a year since that program was discontinued. So a lot of the border encounters, up until May 2023, resulted in immediate expulsion under Title 42 rather than a Title 8 apprehension. So in 2021, about 60% of encounters resulted in expulsion; 2022, about 50%; and even in 2023, it was running about 30-40% until the program shut down.

The other reason is that a large chunk of the people who do get detained through Title 8 processes end up not staying in the country anyway. Sure, some can apply for asylum, and some are released through a Notice to Appear/Own Recognizance order. But about 40% of them leave immediately. Most of them through the Expedited Removal process - but a big chunk are tossed out under prior expulsion orders, and a non-trivial chunk just leave voluntarily.

And while there isn't enough capacity in the system by a long shot, people do eventually have their hearings and are either deported or granted asylum. Last year about 140K migrants were deported after losing Title 8 hearings, and another 60K were granted asylum.

Of the six or seven million border encounters since Biden took office (give or take), maybe 2.5-3.0 million or so resulted in a Title 8 apprehension (the rest were immediately expelled under Title 42), of which maybe 1.5-1.8 million or so were "catch and release" folks remaining in the country. Over those three and a half years, another half million or so were either deported or legalized.

So, no - there's not "ten million" new people in the U.S. as a result of unlawful border crossings. That's off by at least an order of magnitude.

cbp.gov - Custody and transfer statistics
cbp.gov - Title and title statistics