The bitcoin core we have now won’t go away, there will never be consensus on a bitcoin fork. There are more than enough speculators and idealists to keep the original core going. ETC is also proof the original chain can live on, and BTC's network is much larger than Ethereum’s when it split. ETC although considerably smaller than ETH, has a market cap of 2 billion- double what Ethereum was worth going into that whole mess. Bitcoin’s reasons for forking are less contentious, but the much larger network ensures there is enough dissent to cause a split.
The old chain, the software we’re using today, it will continue to be mined. Someone will always maintain it. Its going to retain a lot of value one way or the other, it can claim to be the original bitcoin which is huge. That value means someone will keep working on it, from now and always. Something with a deficiency that is plausibly fixable, with an infinite amount of time and resources to receive attention, will be fixed.
What the solution will probably look like:
Bitcoin’s scaling solution will be like Ethereum’s DAO essentially. A crypto bank that can hold bitcoins. The process will be simple. You send the Bitcoin bank your 1 BTC and it generates 1 “BTC2” for you on a separate ledger. BTC2 coins operate on a ledger that is ultra fast so no scaling problems exist. At any time, any user with BTC2 can send it to the Bitcoin bank and the auto bank will release some of its BTC for you while destroying the BTC2 you deposit. This way you could always convert BTC to BTC2 to BTC at a fixed equal rate. Eliminating the need to use BTC in all transactions. You can always be using something that is “as good as” BTC and equal in value. It doesn’t effectively change the supply of BTC, it just adjusts how quickly a pool of that supply is able to move.
Fees synced to BTC rates incentivize miners on the BTC2 chain. No fees are ever applied to BTC > BTC2 > BTC conversions to keep the fixed conversion pure. In this way BTC fees remain the same whether you’re using BTC or BTC2, again to ensure the fixed conversion rate between them.
It would need to function perfectly. If the process of conversion is delayed at all, or was suspect that it could crash/be hacked, a separate price for BTC2 would develop on open markets. This would probably happen on pure speculation even. Through arbitrage and a perfectly working system, trust would be built eventually and there would be no difference in price, no need to list it separately.
The value of BTC and BTC2 would grow in unison. In the event where 99% of the spendable BTC supply ends up in the bank because people want to use BTC2, no problem. The inferiority of the old Bitcoin technologically doesn't impact its price at all. At any time, even if you're the last guy holding the old BTC, you can convert it for BTC2 and its as valuable as anyone else's money.
Bitcoin becomes lightning fast, no one needs to change anything or abandon anything.
I'm sure someone has already proposed that solution, and other theoretical things that would work. This core won't be abandoned, we'll see something implemented in time.
It may be 30 years from now and Bitcoin Classic is the 20th valued coin, there are 5 new forks of bitcoin, but still the solution to today's scaling problem will come. Creating a second, third, fourth Bitcoin with different parameters will never change that.