I am thinking of the modern games I have played that used classes.
Top Secret(1e) had three classes: assassin, confiscator, and investigator. Gangbusters had classes based on profession as well, Criminal, cop, reporter, etc. cyberpunk did also, though that wasn’t modern when it came out. Other “modern” type settings had classes based on what type of person you were. Star Frontiers had people who were good at tech, good at fighting, and good at interpersonal stuff. Gangbusters B/X has Brutish, Educated, Connected, and Street Smart, all denoting more of a personality or background that shaped a character, than actual skillset.
Finally, there was D20 Modern (not Old School I know, but worth a mention strictly for analysis sake) which had a class based on each attribute: Strong hero (good at fighting), Smart Hero (thinker), Wise hero (basically a healer), Fast hero (dexterous guy), Tough hero (can take a beating but not as good a fighter as Strong hero), and Charismatic hero (the leader/face). D20M had skills that were easier to buy if it fit your archetype, but you could basically have any skill. Other than that, the system was a hot mess.
So let’s look at what the Classes are supposed to do. They help each player determine what role they would play on a team.
It would be easier for everyone involved to have classes associated with role in the group or profession as that would help a player fill that role and act in ways that played to their strengths, this way you don’t have the skinny smart guy with mo martial skills trying to go toe-to-toe with thugs while the big hairy stevedore who competes in prize fights, tries to disarm a bomb.
A more complex game would allow players to choose “whatever they want” or have some die rolls assign weird skillsets to simulate their previous lives prior to becoming adventurers. This would increase character creation time and facillitate more investment into a character. It might detract from a game with a high turnover (death) rate.