The TLM undoubtedly has baroque externals (thinking here of decorative elements and esp. when the music goes over the top), but there remains a no-nonsense Roman core of simplicity and economy. It's easier for me to see near the altar than for the pew-sitter, I'll grant you. There are also remnants of Byzantine court ceremonial (the bows, the maniples, etc.) which are especially pronounced at pontifical liturgies.
Your point about art is well-made. The academic styles quickly become insipid except in the hands of the greatest artists. In sacred art the key thing is that the artist be a believer all the way down. That's something that can emerge in the occasional genius, but most reliably appears in a monastic setting -- which goes to explain the power of eastern iconography.
Would you remind me of what that lonesome Madonna on top of what looks like a white pyramid of flowers, in Mexico? It is on my rosary, but I’d like to be able to see her on the ‘net.