Proof of Stake and Lightning Network require private keys to be online, so both are security disasters. No wonder they are getting support and funding from certain headquarters.
Proof of Stake only requires a wallet be online if staking or sending coins.
Proof of Work only requires a wallet be online if sending coins.
If a PoS user is not staking, then his wallet is functioning the exact same as a PoW wallet.
Staking is optional.* Both PoS & PoW users can make paper wallets if they so choose. *LN is an offchain network, where bitcoin deposits were Time-locked earlier.
Proof of Stake is nothing like LN, so you have some personal research to do , to get up to speed with reality.

FYI:
Please give me the contact info of this supposed headquarters that is funding me, because so far no one has given me a penny. 
And if you want to see the results of endless rewards and why it is a failure,
look at mooncoin or newyorkcoin, both PoW coins.
Mooncoin claims to have an eventual emission of
INT(0.29531*INT(19697202017/(INT(nHeight/100000)*100000)))
which becomes 0 at height 19697300000, so it's not not endless rewards.
Anyway, your argument would be better served by looking at less obscure coins with uncapped emission, such as Monero. Please explain how Monero is a failure.
Monero
1. No blockchain can be public and forever hidden,
anything they store publicly will eventually be broken
https://cointelegraph.com/news/monero-transactions-history-can-be-revealed-and-exposed-researchSo anyone that uses them should be prepared for it all to be public within 3 years from the date of using it.
2. The mere facts they try , keyword
try to be anon, makes them completely counter to all of the worlds KYC/AML,
this means certain countries will block their citizens just for that reason alone.
https://www.investopedia.com/news/japans-fsa-bans-private-cryptocurrencies/3. Bitmain was selling an ASIC capable of mining Monero,
Monero changed the algorithm to disable the ASIC ability to mine monero.
But the fact is , a Monero ASIC was created and bitmain can modify it's original asic to support the changes, the only difference is now they are smart enough not to publicly acknowledge it, they will just keep it quiet and out mine everyone in monero with just a few asics.
PoW is always a winner take all dead end.
* Note: Monero being a failure is not a supply issue because of endless supply generation, but a failure it still will be. *
You're trying to imagine Game Theory will protect bitcoin ,
and it would if bitcoin was the only network the miners could mine.
But since the Miners have access to mining multiple networks, they will be true to their greedy nature and play them against each other,
untiil they decide for certain which one gives them personally the most profit.
Which due to the decreased rewards and ever growing reliance on transactions fees,
the transaction fees profit will lead the miners away from bitcoin as LN will dominate it's fees.
There's very little to no competition for Bitcoin's hashpower which probably won't change for two reasons:
1) Transaction-fees-only from a highly valued cryptocurrency is still more profitable (ie. able to pay for more hashpower) than transaction-fees-with-block-subsidy from a cryptocurrency that has very little value. LN is unlikely to "steal" fees from miners as there's still transactions to be made and mining fees to be paid -- just shared across a much larger user base, decreasing the cost for the individual. That's if LN succeeds. If it fails its impact on mining fees will be -- obviously -- nil.
2) The largest cryptocurrencies sharing their hashing algorithms with Bitcoin are (currently) Bitcoin hard forks that follow the same emission rate, so they have no advantage in terms of transaction-fees-with-block-subsidy vs transaction-fees-only. All other SHA256 coins are way out in the water, the introduction of new SHA256 coins (apart from the stray Bitcoin hard fork) is unlikely to happen.
That being said, what's your opinion on Ethereum's Casper?
The funny thing is , it is the miners keeping the competition alive.
BCH & BSV exist because bitcoin miners won't let them die, because if the miners felt as you do , they never would support another coin,
but the fact is they do and their reasons won't make bitcoin hodlers happy.
First question to all PoW miners why are you supporting the competition?
Watch their answers, doubtful any will be truthful.
Ethereum Casper is a Frankenstein design of Proof of Stake using their smart contract system to emulate one,
but not actually be a Proof of Stake like most others that were based originally on Sunny King's original design.
Due to Ethereum useless token creation system and ridiculous smart contracts which is not legally recognized anywhere,
their blockchain size is massively overly bloated.
FYI:
PoW Miners are planning a massive dump the day Ethereum Casper actually activates,
so it will be cheaper a year out from Casper activation.