What would happen if you lied about your age (eliminate the first 10 years from your resume), both at the time of applying for the job and after joining the company? How much trouble can you get in for that? It doesn't seem unethical at all.
It's also not actually legal where I live for the employer to inquire about an applicant's age. After I was hired, the manager did ask me at lunch how old I was, I just replied, "I can't remember". Yeah, he probably didn't mean anything by it and he could probably look it up with HR. But I just honestly didn't feel like it should be relevant to my role at work.
I don't feel like this was unethical, perhaps slightly paranoid at most. Speaking of which, I didn't even tell anyone I had kids until I was out of my 90 day probation period.
Directly lying is a problem still (don't tell them a wrong age), but if they come to the wrong conclusions due to fuzzy data?
I recently filled an online application that asked for SSN and I dropped it right there. You only need my SSN for employer taxes, no way is that part of any job interview.
If you got your SSN at an age other than ~0, you may get flagged as a mis-match when e.g. applying for a new bank account, and it will require a human override to get past.
It might be a bit weird, but I doubt it'll fail the HR filters. You can even do something like call it 'Education and Skills', in which case dates don't even make any sense to include. (Nobody ever says which year they've learned C#.)
I don't really have a strong opinion though. When I last switched jobs a number of years back a friend of mine strongly advocated for obfuscating age as much as possible. I don't even remember how much I did but it didn't really matter because I knew the person running things and a number of the other people involved in the process. So this wasn't really an HR filtering thing.
And unless these things are explicitly checked for, your resume won't look that weird.
[1] If they do, they should stop, because this sort of thing is great evidence for an age discrimination lawsuit, even if you don't engage in age discrimination.