There's no question that the actors are doing a lot of heavy lifting here, but there's also the ludicrously infectious score, and director Brest has quite a deft touch balancing the humour with the trappings of the cop drama/fish-out-of-water stuff. Obviously it's quite funny at times, but when the chips are down it's pretty exciting too; hard to manage silly stuff and still have action scenes with any gravity even/especially in the 80s.
I'm particularly fond of the chemistry on display in the final thirty minutes or so, when the movie goes into full-on cop action mode. But Murphy, Reinhold, Ashton, and Cox (along with Gil Hill in the opening scenes) are so good together the whole time that mentioning any potential problems with script, execution, etc., ends up sounding churlish.
And the pace "crawled"? If anything, the script can probably be faulted for trying to be
too
efficient because it manages to tick all of the requisite plot boxes with more speed (and, under the constraints of the genre, grace) than just about any other example from the era.

Put it in perspective . What films from the 80's do you consider classics from the genre ?

Yes the OP needed to have experienced this in the 80s. I don't know how many times I watched it then, wore out the film on the VHS. Have not watched in a many years, I'm guessing from the OP (who may have a fair point) it has not aged that well.

you were not around in the 80s
it was a product of its time