For bitcoin network to become insecure the miners have to go away not the investors who buy bitcoin. Such a scenario would require the following three conditions:
1. An alternative cryptocurrency with the same exact mining algorithm as bitcoin (ie. double SHA256 of an 80 byte header)
2. Offering something innovative so that people bother adopting it initially so that it can gain some momentum, a higher price and the incentive for miners to switch over
3. Miners migrating to this altcoin quickly before it is 51% attacked to death itself

These 3 conditions mean it is impossible to have what you call "competitor".
Take bcash for example. It is a shitcoin that has the same mining algorithm as Bitcoin (among other things that are the copied). Since it has nothing innovative, it never got adopted and remained a very cheap shitcoin. That means that shitcoin is susceptible to 51% attack (and it did actually get attacked that way). Something that makes it an even bigger shitcoin.

So we go back to what I said earlier: lack of innovation is the reason for lack of adoption.

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Keep in mind that altcoins don't have to use the same algorithm to be susceptible to this attack. If they choose another mining algorithm, then no matter how high their price goes, they can not attract bitcoin miners because bitcoin ASIC can not be used to mine something else.
The best example here is ethereum which uses another algorithm (uses Keccak/SHA3 instead of SHA2). No matter how much they pumped it in 2017, it could not attract bitcoin miners to threaten bitcoin security.

Again we go back to what I said, lack of innovation is the reson for lack of adoption. Ethereum had some interesting ideas but they were implemented horribly which is why ETH back in 2017 was worth 0.15BTC and it is something like 0.05BTC...