> All creatures try their hardest to out-compete everything else.
When we take a wider look at life, this just isn't universal. If you look at ecosystems in very stable environments (e.g. caves), the ecosystem as a whole tends to come into balance over time, where species are not aggressively try to outcompete their competitors, but instead fit into comfortable little niches so that the system as a whole keeps functioning well. In fact, evolution works on the ecosystem scale as well, and systems with aggressive species tend to be very unstable and prone to crashes. In environments with constant change, then ecosystems are constantly changing and competition becomes more fierce, benefiting aggressive species. This is not always the case, so I don't think it's useful to assume that everything is trying to move as aggressively as possible; otherwise evolution would select against species with long gestation periods and tend towards shorter generations and faster growth.
There isn't any particular reason to privilege caves or other "stable" habitats. This is an incomplete understanding of them, anyway. Because caves are nutrient-poor, it is common that all animals there are extremely lethargic. That is not the same as lacking aggression or competition. Cave animals strive to survive as fiercely as anything in the jungle, just at a much slower pace. If a more active predator were to be stranded in a cave, it might eat everything it can find in a week, and then starve. Within months, other animals from more remote corners of the cave would scavenge its carcass and repopulate.
To visualize this, watch one of those speeded-up videos of starfish and sea urchins. At our pace, they are sedentary. At their pace, it's Thunderdome all day every day.
Caves were just an example, and pretty much the rest of your comment actually proves my point. If a "more active predator" enters a cave and subsequently eats everything and dies, then evolution has selected against it. Evolution selects species that best fit the environment, and that generally means species that find a sustainable balance through both internal and external regulation mechanisms.
Your example doesn't require an invasive species. Aggressive species (ones with their consumption and reproduction clocks set "too high") can arise through mutation, too. In either case they spread like cancer and usually take down parts of the ecosystem with them before they are finally selected against. Eventually, ecosystems find mechanisms to limit the damage of cancer-like species and adjust everyone's "clocks" to appropriate levels. Ecosystems that cannot bring their species into stasis experience repeated shocks, are less stable than ones that do find stasis, and often disappear. This is exactly why the long arc of evolution is best understood as a punctuated equilibrium (https://en.wikipedia.org/wiki/Punctuated_equilibrium) rather than a constant drift. Systems that find stasis are more successful than ones that don't. Unfortunately these systems are repeatedly interrupted by drastic environmental changes like geological events. So, the systems that survive are the ones that tend toward balance but are able to adapt to occasional disruptive events. That requires biodiversity that is generally reduced by aggressive species.
> To visualize this, watch one of those speeded-up videos of starfish and sea urchins. At our pace, they are sedentary. At their pace, it's Thunderdome all day every day.
Or look at hardwood forests that develop extremely slowly over thousands of years, despite the availability of plenty of energy from the sun. The slower the system, the better it actually proves my point. Clearly, evolution does not select for the fastest growing, most aggressive species out there. Otherwise starfish and sea urchins would move faster, or be displaced by something that moved faster.
Properly understood, ecosystems are super organisms that require many many moving parts to bootstrap, grow and function. Human bodies are analogous. Your cells aren't trying to "outcompete" every other cell in a Thunderdome situation every day. They are carefully regulated both internally and externally. When those regulatory mechanisms fail, you end up with cancer and you die. Clearly, cell replication rate is a key regulator internal to a cell that prevents us all from experiencing runaway cancer and dying. Clearly ecosystems have species with internal regulation mechanisms as well.
When we take a wider look at life, this just isn't universal. If you look at ecosystems in very stable environments (e.g. caves), the ecosystem as a whole tends to come into balance over time, where species are not aggressively try to outcompete their competitors, but instead fit into comfortable little niches so that the system as a whole keeps functioning well. In fact, evolution works on the ecosystem scale as well, and systems with aggressive species tend to be very unstable and prone to crashes. In environments with constant change, then ecosystems are constantly changing and competition becomes more fierce, benefiting aggressive species. This is not always the case, so I don't think it's useful to assume that everything is trying to move as aggressively as possible; otherwise evolution would select against species with long gestation periods and tend towards shorter generations and faster growth.