I agree, however, that it can be really frustrating to spend a precious several minutes farming or searching for power ups only to lose it all in a freak accident, an unlucky wall spawn, or even just getting outplayed by someone. I think somewhere in between would be the best of both worlds -- maybe losing about a third to a half of your power ups would be a good balance. Then you don't lose all the fruits of your efforts in an instance but the incentive to not die is still strong. Yet dying will still happen frequently enough that the overall level of power ups that people have will be low enough to keep game play fun and reasonable.
I used to play Mario 3 on the NES, and at the time my country had a bad electrical infrastructure, I hated going back to the beginning due to a blackout.
I'm not an expert in game design (just psychology) but from a hedonic perspective I strongly suspect that you should not be stripping players of assets when they die.
In general, the case for "punishing" a player is weak (why cause the user pain?) and punishing them in a way that makes it hard for them to catch up in a highly competitive game is worse. The "Death" counter going up and losing your current position is sufficient incentive not to get killed, or there could be loss of points, or you could maybe strip off a single distance unit from the bombs.
In the long run you might want some sort of way for early players to catch up quickly, like drops near a player becoming more frequent when they're less advanced compared to other players. Meanwhile, ceasing to strip assets when a player dies, or stripping off only a single unit of distance (not number of bombs, having only a single bomb slows down gameplay a lot) will greatly increase game playability.
Especially don't strip the ability to kick bombs. This makes it far too easy for freshly respawned players to be killed.