Does astrology really fit tarot?

I disagree somewhat. It is exactly that considerable work that you speak about that serves to showcase the correspondences to their fullest. Many of the attributions don't work intuitively but they do work when studied and applied. When I do readings I don't necessarily "do the math," as it were, but I do instinctively know what the card means due to my months of working it out.

This is especially true of the Courts that are among the most exciting and complex cards, but it is impossible to get enough out of them without the astrology. They are multi-faceted just as people are, with dominant and recessive traits. The elemental (Kabbalistic) attribution serves to show how their personality traits are put forth (how their "power" is used) but it is the astrological attributions that show exactly what those traits and powers are. Two thirds one sign as a dominant trait, fleshed out by its planets with one less dominant third. The Courts are a truly fascinating study in personality.

Yes.

I think the Tarot Courts and the natal astrological map are BOTH a good fit together for an insight into personality.

Again, they are different views and if they were not they would be the same thing. But some use different views, not in a contentious manner , but to get various views - which can be seen as 'facets' of the same thing .... but each facet will not give the same image nor represent the whole. The more related ( in the 'correspondence field' ) views one has, the bigger picture can be built up.

This is one of the key factors that appears in hermetics, the 'Perennial Philosophy', 'Progressive Liberation', Sufism, and many 'enlightened' systems.