I am also a teacher on a spousal visa. I work for a (rather) large company here that has a lot of expat employees. They get us IMTAs. They can't legally pay us if they don't.
As others have said, the IMTA is for the employer, giving them the right to hire you. Without it, you might be in a legal grey area but your employer is not. They are illegally hiring a foreigner.
Of course, people do teach from their homes privately or teach online through intermediaries. I even know of people teaching in more formal (actual school) settings through intermediaries (a company that gets paid for the teacher and then pays the teacher). To the best of my knowledge, all of these "alternative arrangements" situations place a risk on the person paying the foreigner to work without a work permit. The law just clearly states they can't do it.
People also get IMTAs that they probably shouldn't be able to... going based on the requirements for issuance with regards to degrees and experience that I believe to be correct. If your employer decided to do that... I don't think you'd be in a rush to run out and share the info on a forum.
I do think it is possible for you to find "legal" work over 60 and without a degree. I just don't think every jot and tittle of your paperwork will be true and accurate and properly processed as you do so.