The color coat can be sand blasted off and new color applied, if traditional stucco. Elastameric paint is thick and can help fill the pores, but takes a big airless to spray and would have to be back rolled.
Stucco holds up just fine with a proper paint job and drainage. I have painted and repainted many stucco houses in socal and my uncle did many before teaching me to be a pro. Bad paint jobs can fail and vines or plants can damage the surface and standing water or over watered planters can dame stucco, painted or not. Zinnser primer is the best, not kilz, and behr paint has held up great on many houses when used on stucco, but I have used many brands over the years.
Filling in the pores with paint does make it look better and cleaner....my walls are a bit off white, well originally a color called whisper gray. They still do get dirty. Paint it dirt color and it wont be so bad. Concrete based stucco changes color when it gets wet and is not an absolute uniform color, where paint is a solid color.
Stucco is a lot of work and while i have done lots of patching, for a few walls on my garage, I learned how to do the entire process with the lace texture, from youtube pros. Watch their videos and see how yours can be refinished, then hire someone.
As stated above, I often did scrub finish on older houses and used glue in the mix and recoated over some of mine that was painted. A pro can do that very quickly on entire walls.
There are quite a few textures of stucco and different sizes of sand. Medium or large sand mixes are common here, but look at commercial buildings and modern houses.....some have a very fine finish and some are an even sprayed or floated, or scrubbed finish with no lace.
Stucco is a great option here and it works and does not rot like wood and it is better than the old house look of siding, even though Concrete siding is a thing now. I don't know why it isn't popular across more of the USA.
Post a picture of what your's looks like.