OK ... let's back up a bit ...
How did I 'guess' 60 amps? What does '60 amps' mean?
First off, many homes, even today, require less than 60 amps of 240V service. This is evidenced by the large number of 60-amp services existing.
If it's enough for the house, it ought to be plenty for the barn. Remember, that's 60 amps of 240 volts, or (if you prefer) 120 amps of 120 volt electricity.
Now, let's look at that barn ...
From experience, I can tell you that two consumer space heaters will be needed to heat a small, free-standing garage. Each of those heaters will "use up" a 15-amp circuit. In summer, the air conditioner will use less.
That's 30 amps.
Let's assume a microwave. Good-bye another 15-amp circuit.
30+15 = 45 amps.
Even two guys, using 'big' power tools, will be able to use the same convenience circuit. You can see this on every job site.
45+15 = 60
Just for giggles, let's throw in another 15 amps for a table saw (or welder). I use only 15 amps, as you can't work a table saw and a power tool at the same time.
60+15 = 75
Maybe toss in another 15 amps to cover the lights, the fridge, whatever.
75+15 = 90
We're still well within the capacity of a 60-amp feeder.
That "125-amp" panel is only a 125-amp panel if it's fed by a 125-amp breaker. More correctly, 125-amps is the largest breaker you can use. Feeding it with a 60-amp breaker is just fine.
As far as "diversity" is concerned ....
THAT matters only for the calculation of the house service. In that case, you fire everything up, measure what's actually used, then multiply by 80%. Now you have a figure for the service calculation.
Try to do it any other way, and you wind up counting things twice. The same situation arises with any other sub-panel. You don't "add up breakers" or "add all the loads." The sub-panel is "the load" ... it just doesn't have a nameplate.
If you're building new, using the 3-watts/square foot, etc., is a good way to guess. The more information you have, the better. The trouble is, the real world is not that precise.
"Services" come in 30-amp and 60-amp. There's a lot of room between those two. A 30-amp feeder would very likely not be enough, unless all you had was one receptacle and one light. A 60-amp feed, however, proves itself daily, in powering millions of homes.
I suppose you could consider ratings like 40 0r 50 amps, but why? All you save is -maybe- one wire size. Since I'm a real fan of over-size pipe, what's the point?
The moral is: Don't be overly precise. Unless you're Harry Potter, there is no train platform 7-3/4.