Printers do specialize. Especially in the industry I work in (wide format/specialty.)
The printers I work with all have their area of expertise or some do some things better than others, or some offer items I can’t get elsewhere. No one printer does it all, at least not in house.
Since I’m considered more of an in-house broker than an actual printer, I have a couple dozen vendors I’ve established relationships over the last 25 years, with only a handful (4) that I go to on a regular basis. It seems like everyone these days has a flatbed printer, but I want the guy that buys a flatbed printer then goes to Home Depot and buys a van full of stuff to see what happens when you print on it. Not all wide format print vendors actually have anything wider than a 3meter machine. But there are 16-footers (5m) out there so you have to develop those. Specialty things include digital HPL (only 4 companies in North America,) fired porcelain (not the dye sub trophy stuff,) digital image powder coating, extra large photographic process (72"x120") and once in a while using the machine over in Stockholm that can print 40’ x 160’ seamless (though I’ve never done anything quite that large, but it’s out there.) Then you can veer off into other things like structural metal sign work and custom metal lettering etc.
The whole process builds from a few small, non-color-critical, non-rush jobs and slowly progresses to more and more complex things. It’s a learning process both ways, but it’s up to you to learn their work flow process and make their lives as easy as possible.
I do use online printers very occasionally, but I don’t do a lot of conventional CMYK press stuff so the options are limited.