I don't know how to help you see it better other than getting out in the working world--I see it everywhere.
No need to insult me. I AM in the working world, and we also earn just below the poverty line and live in working poor neighborhoods and communities. When someone pays a nanny under the table, they are in no way paying more + benefits + bonus compared to what the legitimate jobs are offering right now. Perhaps they were paid more during the pandemic when well off and entitled parents realized they couldn't bear to be around their spawn all day if the kids weren't at school, and when most daycares were closed, but that didn't last. To think otherwise shows very little first hand experience with how off books workers are paid and treated. Both my spouse and I are in industries that novices often enter off book. They don't stay that way for long, as it gives the "bosses" a means to overwork them and then outright refuse to pay. My parents owned restaurants, and a lot of their workers came to them after a stint of under the table work -- usually relieved to finally get an above the table job where they would be protected, paid, and given some form of state benefits in the event they lost their job.
Working "illegally" is a lot more work and a lot less lucrative for most than taking a traditional above board job. Sure, there are exceptions, but likely not near enough to be a driver of wages. This is why most off books jobs are farmed out to undocumented immigrants and those with criminal histories -- in other words, those that don't have many above board employment options.
Your argument was that wages are being driven due to an increase in under the table employment due to the pandemic. A few nannies doesn't an increase make. Construction and restaurants have always hired off book to some extent, so no change there (except restaurants aren't hiring off books, they are struggling to hire anyone in many locations).
I think I actually get your position, whether you are being honest with yourself about it or not -- Government benefits are bad. Poor people will just cheat the system if given half a chance.
Those people are lazy and will take the easy way out. It shows in this quote: "We're all honest folks--no need to cheat the system here--but for plenty of folks, there are all kinds of incentives to cut corners and cheat the system some, especially the tax man." Well, as a poor working class human that has taken advantage of many government benefits over the years to improve my life and the future prospects of my family, I really have nothing else to say. I'll just take an uniformed opinion as gospel because you have top secret anecdotes, and all I have to offer is lived experience in the very industries and fiscal classes at question.
Jeez.