The SSME is an exceptionally complex engine, producing a very large amount of thrust from a compact package. It's working much closer to the margins of what is possible than any of your points of comparison. This was largely a result of a very ambitious specification; in order to reach the required thrust-to-weight ratio and high specific impulse, it had to run very close to its mechanical limits, whereas less ambitious engines can run under less stress. Imagine two identical car engines, one running at 3000 rpm, the other at 6000 rpm. One's definitely going to win the race, but you're going to want to inspect the engine afterward.
According to Wikipedia:
since NASA was interested in pushing the state of the art in every way they decided to select a much more advanced design [for the SSME] in order to "force an advancement of rocket engine technology".
In retrospect, NASA may have gone too far with this strategy; SSME development was challenging and expensive, and as you note, the engine required more maintenance than was ideal for a reusable launcher. Unfortunately, the size, mass, and thrust of the engines was fixed in the specification before it was known how hard it would be to build and operate them. A less "bleeding-edge" engine design would have cut severely into the space shuttle's payload.
In some alternate universe, NASA somehow got a budget to develop the space shuttle without having to cave to the Air Force's requirements; this one has a smaller payload bay and stubby wings like the X-37, and maybe it would have used a simpler engine that didn't need as much maintenance between flights.
This is appalling compared to even the most primitive turbojets
The most powerful modern high-bypass turbofans in the GE90 family produce around 500kN of thrust from an 8.7 ton engine; SSME produces 1890 kN at sea level from a 3.5 ton engine. The GE90s rotors run at 2355 rpm and 9332 rpm; the SSME has four turbopumps; the slowest turns at 5150 rpm and the fastest at over 35000 rpm -- almost 600 revolutions per second.
the engine of the Breeze-M burns for 50 minutes
SSME produces 100 times the thrust of the Briz-M's engine. It has a lot more heating to contend with. Over the course of its 8.5-minute burn it moves about 10 times as much mass through its pumps as Briz would on a 50-minute burn. Briz-M's engine has a thrust-to-weight ratio of around 27:1; SSME around 73:1.
(though not really comparable due to its pressure-fed
radiatively-cooled nature) the Shuttle's own OMS was rated for 1,000
restarts and 15 hours of run time.
OMS uses a remarkably simple engine. No regenerative cooling, no pumps, as you note; as long as the chamber remains intact, the only points of concern are the valves, which operate under relatively low pressure. I don't know how much work was done on these between flights; it would probably be possible to swap out the valves for brand new ones every time at a tiny fraction of the cost of the SSME inspections/overhauls.
the reusable XLR99 had a MTBO of >1 hour
Again, a fairly modest engine that didn't have to achieve anywhere near the performance of the SSME.
Was this removal and overhaul always truly necessary?
This, I don't actually know.