Seems like bad timing, the transaction fees compared to other crypto currencies are massive right now[1] and the transaction speed is just as bad, with 70.000 pending transactions[2]. Im assume that this situation is going to become better. Apparently one reason is, that segwit transaction space is barely used at the moment.
I think you're assuming that Square is going to do all of bitcoin transactions on chain.
I reckon they will handle most of these in their internal ledger the exact same way they handle USD type transactions. BTC could only move from the core secure wallets when BTC are leaving their systems.
There is probably no other way than to do it off-chain. I guess the transactions required to send your bitcoin to a wallet(if this feature will be enabled) might already be a problem. but this brings us to the entire bitcoin as a store of value idea, square will probably avoid the fees with bulk purchase of bitcoins. I have a big problem with that, bitcoin block rewards relative to the total value of bitcoin are going to decline over time. After the 2020 halving the block reward will be less than 2% the value of the network[1]. i assume satoshi imagined that overtime people will use transaction fees to secure the network. with bitcoin core moving to off chain solutions with no fees, i dont see how this will work out.
Bitcoin has increased so much in value that those tiny transaction fees that you paid are now worth a lot of dollars. It's a problem all right, but it's a comparably nicer problem to have than a cryptocurrency that isn't worth as much or that isn't as heavily used or both.
Er, no, bitcoin going up is nice if you hold bitcoin like gold, and irrelevant if you imagine actually using bitcoin as a way to do transactions. Bitcoin going up or down in value relative to other cryptocurrencies is orthogonal to the problem that it is inconvenient and expensive as a way to move money.
[1]https://bitinfocharts.com/de/comparison/transactionfees-btc-...
[2]https://jochen-hoenicke.de/queue/#24h