Being "into that kind of thing" might take one into esoteric realms. Cf. Mercury (Hermes, Hermanubis) as the psychopomp, or conductor of the souls of the dead.
I take your point that you could read a horoscope in a completely workmanlike manner.
But once we start asking why questions, then the mythological cosmos beckons.
Why does Mercury rule liars and thieves?
Why does Mars rule soldiers?
Why does Saturn rule the elderly?
Sure....
But remember (and this is not to be exclusionary) that you're on a traditional subforum. The mythological cosmos doesn't really play into the predictive nature of traditional astrology. I'm actually understating it, it almost never plays into the predictive nature of traditional astrology. I would actually argue that delving into mythology would get in the way of the concrete interpretations that traditional aims for.
I'm sure that one could come to all kinds of insights through meditating on the mythology tied to the planets and especially the mythology tied to the constellations and fixed stars, but that kind of meditation is more in line with modern practice than it is with the predictive nature of traditional. If someone wants to know what their chart says about what kind of career they're inclined toward or how likely it is that they'll get married, mythology isn't much of a factor.
There's nothing wrong with being interested in mythology, but I disagree that not incorporating mythology into your delineations necessitates that you're reading the chart in a "workman" like manner. Traditional astrology is rife with analogies and metaphors that have nothing to do with mythology. Factors mean things because of metaphorical similarities that they have to other things. Even Ptolemy's physical language is very vivid , giving the planets and signs a richness that rivals what one would get from mythology. His language is distinctly agricultural, rich and down to earth but also very practical. Astrology is by its very nature a system of analogies.
You can start asking
why questions without resorting to mythology. It's very bold of you to assume that investigating mythology is the only way that people can be reflective about their astrology. Ptolemy chose to ask these questions by resorting to Aristotle's physics. Ibn Ezra asked those questions by combining Ptolemy's stuff with astronomical factors. The writer(s) of the Picatrix chose Neoplatonism. Mythology is just another way of doing the same thing, but not the only way and at times not even the best way.
There's nothing wrong with liking mythology, but I don't think that it's the bread and butter of astrology. There are tons of other analogies and metaphors that one might find useful for different purposes. If you're aim is more one of introspection then mythology is probably going to be great, hence why it's so popular in psychological astrology. If your aim however is prediction and the analysis of concrete events (past, present, or future) then mythology might only obscure things when more concrete language is necessary.