I think the answer is twofold: 1. These systems are a good one-size-fits-all to try first---if it ain't broke, don't fix it; and 2. People are very dogmatic, especially when they lack experience. They see these systems in the lab/literature and use them, the work, and they end up in the literature again.
To answer your specific question, people do. EtOAc/DCM is actually a good system if you want something with more dissolving power than an EtOAc/hydrocarbon system but an eluent that's less polar than a DCM/MeOH system. If at all possible I prefer EtOAc/MeOH to MeOH/DCM as it's way less toxic and doesn't go through gloves so fast.
Miscibility can also be an important factor: methanol/hexanes don't mix well, and acetonitrile/hexanes are totally immiscible, so don't waste your time on those. I saw a first year grad student run a column in methanol hexanes once -- she literally ended up with biphasic fractions in her rack of tubes. Very funny.
There are so many good alternatives if the off-the-shelf systems don't work well. Subbing toluene for hexane in EtOAc/hexanes is a great, slightly more polar alternative with much better dissolving power for (poly)aromatic compounds. Acetonitrile/toluene or acetone/toluene are also great for more polar compounds. Toluene/hexanes is nice for apolar polyaromatics---I had great success separating regioisomers of a bromonaphthalene in this.
Sometimes you get desperate and try odd mixtures. A labmate of mine just ran a column in hexanes/THF as it was the only thing after 6 hours of TLC-ing that separated her diastereomers. I ran a column in MTBE/i-PrOH/Hexanes a couple of years ago for lack of anything reasonable that worked.
My PhD supervisor said that during his graduate studies in the 70s, acetone/CHCl3 was a very popular mixture, but it's fallen out of favor as CHCl3 is kinda toxic and those solvents will react with each other in the presence of trace base (the Bargellini reaction).
There are a few wacky options too: I have columned N-alkylpyridinium salts on silica in aq NH4OH/MeOH/AcOEt, and the famous 4:1:1 n-butanol/acetic acid/water is a classic for purifying unprotected amino acids on silica, although god knows that's it's a pain to rotavap down. I'd also add that 4:1:1 is also good for biotinylated molecules, which are far more polar than they have any right to be.
So I guess what I'm saying is: as you gain experience, and work with tougher mixtures, you'll end up branching out. But EtOAc/hexanes usually a good way to start. And as I'm a process chemist, I should also point out that recrystallizations and distillations are good options too!