When you commute a prisoner’s sentence, it becomes shorter. What does that have to do with commuting to work? I saw this description of the etymology from podictionary: word of the day commute

… A commuter is of course someone who commutes. Commute as a word took the trip into English first in 1633 from Latin commutare and it didn’t have to do with traveling, but change. The original English meaning was such that people would commute money at a currency exchange.
Thus the original Latin meaning of change shows us that commute is related to mutate. It also explains how a felon can have their sentence commuted, usually meaning changed to a less harsh punishment.
The word first took on a meaning of traveling back and forth about 100 years ago. As EB White wrote of commuters:
One who spends his life
In riding to and from his wife;
A man who shaves and takes a train,
And then rides back to shave again.
I noticed an interesting 100 year old citation in the OED. A British newspaper explained to its readers that commute is the American term for “taking season’s tickets.” To me, season’s tickets means a sports season but this citation refers instead to something like a transit pass. In the quote the commute is by train and between New York and Chicago, so it’s not likely something undertaken twice a day.

Etymonline
says

commute
c.1450, from L. commutare “to often change, to change altogether,” from com- intensive prefix + mutare “to change” (see mutable). Sense of “make less severe” is 1633. Sense of “go back and forth to work” is 1889, from commutation ticket “season pass” (on a railroad, streetcar line, etc.), from commute in its sense of “to change one kind of payment into another” (1795), especially “to combine a number of payments into a single one;” commuter is from 1865; the noun commute is from 1960.

So it is all about change, a commuter changes money into rail season pass tickets, or in other words, increases the fixed cost of his trip in order to lower the per trip variable cost. At some point, commuter took on the connotation of journey to work (we don’t commute to the store, though apparently we once commuted between cities).
Today we talk about auto commuters, who don’t buy tickets (except perhaps on toll roads), and the standard policy prescription is to encourage them to pay out-of-pocket for the marginal social cost of their trip (and discourage auto ownership through techniques like car sharing). We may then have the reverse of the earlier meaning, where we exchange a high fixed cost/low variable cost scheme for a high variable cost/low fixed cost one. Perhaps we should rename people who do that from commuters to commutees or commutants?
(As an aside, it surprises me that commute was not a noun until 1960, just like gridlock did not appear until 1971 or so).