Well, that all depends on the car. Once upon a time, I had a 2003 Nissan Sentra SE-R Spec V (yes, I know). I did a few mods to it, one of which was rear engine mount insert (same as what we're talking about here) because that car also suffered from idiotic amounts of wheel hop when you tried to launch it hard. The amount of flex in the stock mount was unbelievable. The mount alone made it a bit buzzy, but I could live with that, because it was 2003 and I was young and I didn't know any better.
Later on, in an attempt to get that lazy, slow-revving slug of an engine to respond to the throttle a little better, I removed the OEM accessory drive pulley and replaced it with an aluminum one that didn't have a 12lb weight on it... And you can probably already see where this is going.
From then on, the NVH in the car went from bad to worse to intolerable. It wasn't the smoothest engine to begin with, but removing some of the things designed to dampen the vibrations was not smart. When the A/C was on at idle, you'd swear the engine was running on crushed up cinder blocks. By the time I got rid of it, the interior had more squeaks and rattles than a 1980s Ford, thanks to all the added vibrations.
I would say that I single-handedly ruined that car with my careless modding, but some credit is also due to the #3 piston, which decided one day to try to eat its way out of the engine.