It's a bolt action rifle. Slow and must of the time you lose sight picture because of changing the bolt. Especially in intense urban areas, bolt rifles seem like the wrong choice.
The answer's a bit complicated and rests mainly in different priorities. In the grand scheme of things, infantry service rifles are fairly inconsequential compared to most other military equipment. Speaking broadly, as long as the service rifle is "close enough" in capabilities to what the opponent has, the impact any difference in quality has is negligible compared to other factors.
In the case of Germany, their rearmament in the leadup to WW2 had placed priorities on areas other than service rifles. Aircraft, vehicles, artillery, and machineguns all had the potential to impact the battlefield far more than a more effective service rifle, and with every other power in Europe nowhere near adopting a semiautomatic rifle, there wasn't much reason to push heavily for such development. General infantrymen may have been limited in capabilities with a bolt-action rifle, but it was believed that superior machineguns (and an infantry doctrine centered around them) would more than make up for that, and any close-range fighting could be handled by the limited issuing of submachineguns.
Unfortunately for the average German infantryman, you're spot on with your assessment that a bolt-action rifle is poorly suited to city combat. However, prewar planners didn't really have any expectations for city combat prior to WW2 - rather, they expected largely a repeat of WW1, where the long engagment ranges of bolt-action rifles supported by machineguns was needed to keep no-man's land clear, and submachineguns were a tool for assault elements to help clear trenches.
By 1940, we start to see a reevaluation of these priorities as a result of wartime experience. Germany finally kicked off a serious semiautomatic service rifle program, but they fell for some of the same traps a lot of other powers were caught in with early semiautomatic rifle attempts. Namely, they wanted:
Mauser and Walther would both develop rifles for these requirements (although only Mauser would actually follow these requirements to the letter), but even the more practical Walther G41 design suffered from quite a few design flaws that weren't resolved until the major redesign that resulted in the G43. Around the same time as the G43 coming into existence, we'd also start to see the development of what would become the StG44, which pulled even further with wartime experience that showed that standard rifle cartridges were overpowered for normal combat ranges and volume of fire was critically important.
While Germany was certainly a bit behind the curve, having waited until 1940 for a serious semiautomatic rifle effort to get into motion, it's not exactly out of the ordinary. The US really stands out as an exception with the adoption of the M1 Garand, and the only other major power to adopt a semiautomatic service rifle before entering the war - the Soviets with the SVT-40 - ended up having to revert back to the Mosin due to the expense, wartime demands, and critical failings in the rifle itself. While the Soviets ended up mostly reverting back to the Mosin (though they kept SVTs in limited service), we'd see similar developments on both sides of the Eastern Front with respect to infantry rifles. Combat increasingly became decided by close-range engagements where volume of fire - rather than effective range - was critical, and so the Soviets began issuing submachineguns in larger numbers. Meanwhile, Mosin Nagant cabines began to replace full-length rifles to retain longer effective ranges while improving handling in close engagements, and work even began on the same kinds of intermediate cartridge developments that we see leading to the StG44 in Germany.