Typical for WW2 Germans. When they realized that the main problem of guided missile is exactly guidance, they have no better idea than "erm... let's put a pilot inside, so we don't need to dig into this spooky electronic stuff".
Not exactly. By the end of 1943 it was clearly apparent that they--Germany--had fallen far behind the US and Britain in the development of electronics. Their available radars were barely adequate as part of a missile guidance system. They (they didn't know about this set yet) had nothing like the SCR 584 that could be locked onto a target, automatically track it, and compute a firing solution. Their proposed MCLOS systems were nearly worthless as practical guidance systems.
Because their electronics industry couldn't even come close to meeting their current needs, there was little room for R&D on any sort of large scale and no capacity to build the guidance systems even if they could design one that worked. An automatically guided missile was not going to happen for them anytime soon.
The alternative was a manned SAM. Werner v. Braun and Walter Dornberger proposed just that as early as the end of 1941 but got turned down hard by the Luftwaffe. Erich Bachem made the same proposal in 1944 and was initially turned down. It took Himmler's intervention to get his proposal authorized. This resulted in the Ba 349 Natter. This was for all intents, a manned surface-to-air missile. The pilot was needed for terminal guidance and attack of the target in lieu of an adequate guidance system with sufficient accuracy to get the missile there and the lack of a proximity fuze to kill the target. The system was sufficient to get the Natter to the vicinity of the target automatically where the pilot would then take over and make the final attack. Because it wasn't to be a suicide weapon, there were minimal provisions to save the pilot and rocket motor in the face of increasing scarcity of resources.
I have little doubt that if the Japanese had been shown the Natter and had gotten plans for one, they would have enthusiastically adopted it
as a suicide weapon.
As for Messerschmitt and the Enzian, it's very likely that if it were proposed as a disposable manned interceptor, it would have been turned down just like every other such proposal was. As for the proposal itself, I could see Messerschmitt overselling it, particularly if he knew some rival in the industry was proposing one. But given that the Enzian had major, unresolved, issues with its engine, I can't see a manned one being a realistic solution to the SAM problem.
I would say, a more immediate problem the Germans had, and likely hadn't fully recognized, was their lack of any alternative in solid fuel to double base nitrocellulose (dyglicol). Of course, given the shortage of oil and rubber in Germany, this was probably a self-inflicted failing based on those industries.