For Bethesda, the situation is so bad that if they don't replace the engine quickly enough, each of their games will fall further and further behind new games, which has never ended well for anyone in the long run.
Absolutely not, the day Bethesda switches off Gamebryo is the day of their funeral. This has been discussed at length before, but in a nutshell - losing their modding community will kneecap their reach immediately and they'll face significant cannibalisation from their own prior titles in the long run, and both development costs and gameplay will have suffered immensely as the studio won't have been able to leverage their in-house expertise anymore (Bethesda used to punch above their weight class in terms of staff size).
The main problem with Starfield, as far as I can tell looking in from the outside, is precisely that it seems Bethesda have
not played to their strengths in the design department. It's hard to tell to what extent that's down to their aggressive staffing expansion or their veterans simply not giving a shit anymore, but the issue isn't Gamebryo/Creation Engine's capabilities, it's Starfield's design not being adapated to those capabilities. The studio's been (lazily) building up the engine for twenty years to provide a very particular sort of gameplay experience, one which very few other developers have attempted, it's what we've all been expecting from them and, whether it's Fallout 3 or Skyrim, we more or less got it. With Starfield... less so, I guess?
The shitty engine can't render the terrain fast enough if the player is moving too fast, which is why we don't have any vehicles in Bethesda games.
Why do you think there is no space travel in the game and instead we have a fast travel festival?
Case in point, you're mixing up a bunch of things here - the lack of deep space freeflight isn't an engine limitation, it's a (catastrophic) design choice. The traversal speed limitations in Gamebryo aren't driven merely by terrain rendering, but by all the moving parts cells are typically populated with, from AI actors to various triggers and objects with physical properties. You move everything into space, you've got a lot more headroom and leeway to represent scales and, given there's no landing on planets, there's no reason that Gamebryo couldn't have represented the rest of that fantasy in a sensible fashion.
Most likely, at some point through development, someone just figured that flying between planets wouldn't be that important for the gaming experience they were pitching. They were
wrong.
P.S. Since the videogaming scene's all super erect over "redemption stories" these days - if TES VI comes out in a few years and it's just Skyrim 2 running on a Gamebryo with yet more lipstick, everyone will choom their pants that "Bethesda's back!" Because that's what the engine's purpose-built for, that's what they
know knew how to do and, most importantly, that's what people want from them.