Old school is more an approach to what the system does, and what is the responsibility of the players and GM. FS is certainly not an early RPG design. Many modern game (indie in particular) focus on getting to "the meat" of the story/situation/drama, whatever that given game thinks the meat is.
(For instance a magical girls game based on the Apocalypse Engine has one or two rolls total per participant in a battle. Choose a tactic, roll, accept the consequences, and get on with the story itself. It finds no interest in whether you should have used your piercing three shot area effect 2 meters attack before or after the takes three actions, costs health, once a day attack or the other way around. it expects you to define that detail and drama as flavor only.)
I've only read the John Carter series and perhaps Triplanetary counts, so I can't say i am an expert on planetary romance, but FS does not remind me of either. I think the goal of Adventure! fits, less sure about the execution.
Is there a game where it is easier and more effective to be a generalist? Even games with increasing cost curves only de-incentivize being a generalist, but you still benefit if you can do everything a little bit. I suppose you could drop below the threshold of usefulness for adventuring purposes (high difficulties).
I think that for the most part you can use FS, or many other similar systems without issue in the setting. It is convenient that there is a game (FS) already used to describe the setting in some detail, and your players won't care as long as you allow all the gear, or n one of the especially weird/difficult to defeat without a specialist item stuff.
If you want a more mechanically satisfactory experience, you have a huge task no matter the system chosen.
I'm glad it works for you. I only say anything because I don't think the game as written does anything in particular, and if you think so, you may be one of the few , and want to double check. If you are sure, then get on with making/supporting/calling for what you want, and pay me no mind!