Lumen_99

The most important points from a management perspective would to me be
Who will manage and maintain said servers? Do I need to hire someone for that and how much will licensenses and maintenance cost? How much time and money do I need to waste getting people used to the new system? Why should I spend much more money on a server vs a few loose drives? Who will manage and maintain said servers? Do I need to hire someone for that and how much will licensenses and maintenance cost? The thing about "money isn't an issue" is that it's often indeed not about the money, which is usually there, but about the justification why one should spend it. Especially number 1 and 4 are of huge importance.
How clearly (read basic) have your pitches been in explaining how a server would solve this? Relatable examples help strengthen a case. You can't convince them with just "a server would fix this". Show them the actual problems, how they affect the company, how you propose to solve them and then what it might cost. For example:
Are they aware of this in simple layman terms? Might there be paper trails from emails etc. of people asking where what is or what the latest version is? Of multiple people working on the same thing? Of unfortunate delays because a drive went missing?
 
Finally, baby steps. Don't try to too radically change the system in one go. For example, people working off their machine or portable drives may be fine with the tweak that every day you synchronise your progress or backup drive with the main server. This can be tied into the previous points by pitching central data storage, less risk of random data going missing and how data is protected against drives breaking (if in a RAID or RAID-like setup) and people losing them. And at the end of the day they say no, then not much you can do except try again if they're not annoyed yet or let it be.