i doubt the Andorians and Vulcans would be biologically compatible even in Trekverse, since they're blood chemistry is so different.
In the VOY episode where Torres fixes a robotic soldier (can't remember the name of the episode), she goes to the EMH for help with the problem and he mentions about how a Vulcan and a Bolian couldn't transfuse blood without killing the patient.
It might be the same for Vulcans and Andorians, though a Bolian-Andorian hybrid may be more likely.
As for the point about interspecies breeding being absurd, I do agree that it is a little far-fetched that humans and species just happen to share enough genetic similarity to produce healthy children. This could go back to the fact that all humanoids came from a single species (a TNG episode whose name I can't remember either). Or when Jadzia and Worf were planning a family (just before she was murdered by Dukat), she had to undergo ovarian-resequencing therapy in order to conceive.
Just a few thoughts.
Andorians and Bolians have (what should be) yellow, cobalt-based blood while Vulcan have green (should be verdigris) copper-based blood. Fan fiction also has andorians requiring 4 genders to procreate and have completely different circulatory systems.
I too loathe Trek's decision to use half-breeds as often as they did. Spock was an anomaly (how can a mother with iron-based blood keep a foetus with copper-based blood alive) but I could accept him as a one-off because it was the sixties, he was useful as an allegory, and the nature of the Vulcan psyche led to some interesting confilcts (although later writers managed to tell the same stories perfectly well with full-blooded Vulcans). Saavik is fine as both species have a common genetic history.
Deanna - dreadful. Kheylar - awful. Sela - pulease. Naomi Wildman - drown at birth. Active genetic engineering would be needed to produce these hybrids. But hang on - the Federation has banned genetic engineering...
I think writers often used it as an excuse to avoid making their aliens too alien or (e.g. in the case of Deanna) as a way of limiting an inconvenient racial trait. Of course I view that as one of the show's flaws. If you don't want your aliens to be alien, then don't use aliens in the first place.