Tough crowd...
As the prior owner of a 3yo and the current owner of 3yo twins, they’re not unbreakable but there’s a lot of difference between them and a lot of difference from just-3 to almost-4. I’d also worry about crashing more than about “shaking”
I chose the MTB I have because it was good for towing a trailer but could be easily upgraded into a much better bike later if I want to. I expect to buy full suspension again someday.
Added on edit: if you do decide to try it, you will really benefit from a dropper post. 150 is good. This is not the usual dropper post advice, it's a different situation, but I speak from experience with a
Thule kid seat on a city bike. The kid seat is right in your standover. Front seats without a dropper require you to lower the seat completely so you can flat foot the bike or do cowboy starts and stops every single time.