How urgent is it to resolve two-prong problems?
For older appliances and such, pre-electronics, it's only a safety issue and even then, only under the worst case scenarios. The National Electric Code is all about those worst case scenarios however, hence the requirement. I'm not minimizing the safety aspect, I'm just saying that people survived for a LONG time with 2 prong outlets.

That said, the OTHER issue (which was not really an issue when the change was made) is that electronics, or more specifically anything that uses a "Switch Mode Power Supply" (SMPS), needs to have a solid reference to ground so that it can deal with what's called "Common Mode Noise" created by the power supply itself. Now virtually EVERYTHING you see with any sort of electronics in is has a little SMPS, all of them creating CM noise on the line. With no reference to ground, that noise builds up, potentially degrading the life of your electronics. So the longer you wait to fix it, the shorter the life of your computers, TVs, phones, "smart" appliances etc.

But per that other thread, in a lot of cases, older houses were wired with what's called "BX" cable; flexible metal covered conductors, and that was grounded, then the outlet and switch boxes were steel as well, all connected together. So if that's what you have, AND you have a metal screw (not plastic as they are now) holding the cover plate on, you WILL get a ground connection by using those adapters and attaching them via that metal screw.

Here is a better thread illustrating this concept.

What is the purpose of the &quot;grounding&quot; tab/wire on a 3-prong to 2-prong adapter?