For example if you use

  \usepackage[spanish]{babel}

to change the hyphenation tables, it also change a lot of things. For example it makes < and > active characters, so they can be used as a special kind of quotes. This breaks other packages like xypic that expect that < and > are normal characters to recognize the arrows.

Yes, now most people use online services that run on a standard platform with the dependencies already sorted out.

I've been using LaTeX for almost a decade and never faced this problem. Always done ```sudo <insert package manager and options> texlive-full``` and been good. Only dependency issues I've faced are forgetting to copy a cls file (which are downloaded).

I have run into that problem, but only when merging Latex documents with different packages. If you find something that's really difficult and requires a lot of packages, ask why other users haven't made it easy already - maybe it's not a good design.