If services like Bitpay start allowing alts, then Yes, I can see alts overtaking bitcoin. We've already started to see the major exchanges like coinbase and co start listing alts, it is only a matter of time till all the surrounding services allow alts as well, and then the market can decide.
Even when Bitcoin fees were palatable for everyday transactions, hardly anyone was doing them.
Bitpay themselves say that more and more transactions are B2B. I don't think that's mainly down to the fees squeezing out the little guy. It's overall a better fit for that purpose. In that scenario a $1 fee for something that's done and dusted within an hour is still a vast improvement over conventional banking.
If you've got a debit card then there's no point in paying in BTC unless you have a huge gain you want to splurge or you're simply doing it to support the concept.
It won't be business or merchant usage that causes Bitcoin to be eclipsed, if it ever is, it'll be the speculation that's been driving this thing since the early days.
And in the case of big business using alts, most of the time it'll be like ETH. If you look a little closer these alliances are lifting the code and making private versions. A nice endorsement but not much more.