Is it intended that bitcoin miners will take over PoX mining?
Not intended, but this is a degenerate outcome of the system that could happen if every Bitcoin miner decided to (1) participate in PoX mining and (2) decided to block everyone else’s block-commits besides their own. This degenerate outcome would be equivalent to running the Stacks blockchain as a 100% merge-mined chain (so, the system would keep working and would be backed by Bitcoin’s hashpower, but transaction-inclusion would be executed only by Bitcoin miners). PoX would continue to work – if Bitcoin miners did nothing else besides the above behavior, then they would still be obliged to pay BTC to reward addresses.
“Discount mining” is a phenomenon whereby Stacks miners decide to stack their STX, and in doing so, “pay themselves” with PoX. This is IMHO much more of an immediate problem than Bitcoin miners taking an interested in Stacks, because discount miners can effectively monopolize the chain over time through significantly lower mining costs. This is why PoX is not a permanent fixture of the Stacks consensus protocol (it phases out over 10 years), and why Stackers have the option to disable PoX in favor of proof-of-burn on a reward-cycle-by-reward-cycle basis (in order to threaten miners into not discount-mining).
Are there still opportunities for normal PoX miners that don’t miner bitcoin?
If the Stacks chain gets monopolized by Bitcoin miners, but if Bitcoin miners are economically rational, then it would still be possible for non-Bitcoin miners to mine – they’d pay a Bitcoin transaction fee on their block-commit that is equal to the expected STX coinbase. While this would suck, it would mean that non-Bitcoin-miners would still have a say in what goes into blocks.