Transmit/Mac when it's discounted is definitely worth it IMO. $45 is a little steep, but Transmit performs really well, especially when you have a lot of little files to move.
It literally needs to save you about an hour’s worth of time over its lifetime to be worth it. And that isn’t even including all the other benefits you get from using a more frictionless and pleasing to use software.
I find complaints about the steep cost of tools from professionals when they don’t even cost triple digits quite short sighted, to be honest (an exception could be made for professionals from countries where their pay is significantly lower).
One thing I will say though is that there are other costs associated with non-free software beyond just the license cost. You've got to manage license keys. You've got to worry about upgrades. If your company is paying for it you've either got to go through IT for procurement or you've got to submit an expense report to be reimbursed. Sometimes there are obnoxious license servers that you need to deal with (I'm looking at you, IntelliJ!). Installation of paid apps is harder to automate than a simple homebrew or npm command.
Of course, all of this may still very well be worth it if the software is useful.