If they would have wanted to participate as members of the society, they would have come here legally.
Oh wow, why didn't they think of that! Just "come here legally" - it's so simple! Please share with everyone your brilliant plan that nobody thought of! *eyeroll*
And FYI, "being in the US illegally" is only a civil offense. And your entire economy is built around the existence of these people, who subsidize your government paying taxes on services they're legally barred from collecting, and creating vastly more wealth than they're paid (which then goes back into your economy, because economies are not zero-sum games). They're also disinflationary, lowering the costs of goods and services. And tend to work in fields that have chronic massive labour shortages (ag, food processing, construction, etc - there's generally a huge labour deficit there).
If you want to know what happens if you slash production but don't slash consumption, simply look at what happened to inflation the world over in the years following the COVID pandemic.
the (up to) 3 million a year let in by Mr Biden's open-Democrat-voter, er, -border policy,
That conspiracy theory is (A) illegal, and (B) logistically unfounded.
Illegal immigrants cannot vote. In case that's unclear, perhaps all caps will help: ILLEGAL IMMIGRANTS CANNOT VOTE. Only citizens can vote. The punishment for illegally registering or voting is not a slap on the wrist. It includes fines, imprisonment, and, crucially for an immigrant, deportation and being permanently barred from ever gaining legal citizenship. The risk is immense for the "reward" of casting a single, statistically insignificant ballot - not least of which because the vast majority of the immigrant population doesn't live in swing states to begin with.
To register to vote, you must attest under penalty of perjury (felony) that you are a U.S. citizen. Most states require some form of documentation like a driver's license number or the last four digits of a Social Security number to register, which non-citizens and undocumented immigrants do not have.
There has been study after study after study on the notion of widespread illegal voting, and every single time, it's found to be mythical. Even the goddamn Heritage Foundation's own database (which they collect to argue for stricter voting laws) shows that it's a myth. They track every case of voter fraud in every election, and all years together from all sources of voter fraud (not simply "noncitizen votes"), there's only about 1100 cases during a timeperiod were 3 billion votes were cast, and that's overplaying it (it's not ~1100 cases of ineligible people, but includes everything from vote buying to interfering to intimidation to improper voting assistance). The Heritage Foundation itself has only 41 cases of noncitizens casting votes. A voter is more likely to be struck by lightning than to cast a fraudulent vote.
And to reiterate, this isn't some grand conspiracy, it's because it's the worst tradeoff imaginable. The benefits for casting a fraudulent ballot are tiny. You have almost zero chance of swinging the election even in a swing state, let alone a red or blue state. If you even care about the election at all. The penalties, by contrast, are extremely high, especially for a noncitizen. And it's easy to get caught (registration requires verifiable personal information that is easy to crosscheck, and indeed is *designed* for crosschecking - see ERIC for example - then onsite against poll books - plus there's a ton of other things like the "jury duty trap" (jury duty is drawn from the poll lists but then leads to cross-referencing the individual)). It's like trying to hold up a bank to get a single lotto ticket from the vault; it's just a nonsensical risk-reward tradeoff. And on top of it all, the notion that it's party based... you realize that Trump had 42% support among Latinos, right? Latino voters are on average conservative and religious compared to the US average, and have been increasingly swinging toward Republicans. If Democrats wanted any block to come to the US, it wouldn't be conservative hispanic catholic men, it'd be college-educated black atheist women (cue the "This Is The Future That Liberals Want" memes).
Lastly, the "three million per year" number is itself mythical. There's 2-3 million "border encounters" per year. This is a very different number from people who are "let in" (except, of course, nobody is being "let in", they're sneaking past border security). "Border encounters" includes people who are caught trying to enter and immediately returned (e.g. never get in - the vast majority), individuals who attempt to cross multiple times (one "encounter" per attempt), individuals who are legally allowed to enter to claim asylum, etc.