Ethereum and other "smart contract platforms" capable of running turing-complete code and "developer-friendly" mindset and community have been running for years and they were able to produce a very low number of potentially useful "contracts".
What are these contracts, actually? (Considering Ethereum, but others are similar:) they are sidechains that run inside the Ethereum blockchain (and thus their verification and data storage are forced upon all Ethereum nodes). Users can peg-in to a contract by depositing money on it and peg-out by making a contract operation that sends money to a normal Ethereum address.
Now be generous and imagine these platforms are able to produce 3 really cool, useful ideas (out of many thousands of attempts): Bitcoin can copy these, turn them into 3 different sidechains, each running fixed, specific, optimized code. Bitcoin users can now opt to use these platforms by transferring coins to it – all that without damaging the nodes or the consensus protocol that has been running for years, and without forcing anyone to be aware of these chains.
The process of turning a useful idea into a sidechain doesn't come spontaneously, and can't be done by a single company (like often happens in Ethereum-land), it must be acknowledge by a rough consensus in the Bitcoin community that that specific sidechain with that specific design is a desirable thing, and ultimately approved by miners, as they're the ones that are going to be in charge of that.