just because i talk generally about what most crap coins do. and you hav in mind your favourite crap coin that does something else but without realising im not psychic to know which crap coin you are favouring this week. does not mean i have not done my research. it just means i am not talking about your specific crap coin you have secretly in mind.

the transaction fee "burn" of your crapcoin is not a loss to miners. its a loss to people making transactions (normal users)
those staking coins to mine dont lose anything. its like a reserve. they vault their coin. sign a block, if they get to be the main signer they get the fresh mint coin, and even more then that they can take their stake out and keep that too.
generally speaking. though some crap coins dont just burn, but give the tx fees of all users to the miner that one as a bonus ontop of reward.

by having a PoS that burns users coins when they transact. the miner is getting minted coin. keeps his stake safe and now the network has less coin for users, making that miners coin more valued due to scarcity. without any cost to the miner.

so i can see why you love the idea of free money mining.. i see why you want effortless/workless/ lazy mining too.

but here is the thing. if a crap coin was to become popular. there would be less slices of the reward pie to share between miners. as there are only so many blocks and so many rewards to share between. so if a really popular crap coin had 1million miners, but was only making 200 blocks a day of 10 coins a block.. then 1million miners wont be elegantly split a daily slice of 0.002 each, instead the addresses with the most hoard will get most blocks meaning there will be some getting 10coins a block for multiple blocks. and hundreds of thousands of people getting nothing.

this then leads to those hundreds of thousands trying to pool their funds into an exchange wallet cold store and hope when the exchange wins a block due to large cold store hoard, the exchange will split the reward equally.

well i have not seen many, if any exchanges paying 'dividends', 'interest', rewards to its users just for letting an exchange hold their coin.. well not unless they are actually a ponzi..
so just dont expect to get free coin if your crap coin you favour was to become popular.
you are still going to end up with the same elitist problem you think bitcoin suffers from

and also, bad security, centralising funds. and crap value based on 100% speculation and not any real underlying cost

sorry but bitcoin has real value due to real cost. you know real work. real effort. and better security.