The single best use of Koban is, when there is an event with unusually good rewards that you weren't going to get, buying the rations and/or fast battle tickets necessary to make sure you get those rewards. This only applies to events with unusually good rewards. In the current rebellion event, if TruelyNice and Aqua-chan spent all the souls they've gotten from the event on soul tickets, they've probably gotten over 130 soul tickets each so far. That's huge, but you'd better believe that they're burning a ton of koban on fast battle tickets to make that happen.
But the rebellion event (which formerly ran as the crusader event) only gives such great rewards if you can kill the boss in one battle, and the rewards drop off precipitously if it takes you 10 battles to clear it. The other notable event was the last four opponents in the summer generals/water gun event, which had a 0.2% chance of dropping an SSR EVO card. You could only fight them 50 times each, for 200 per day in total, which didn't necessarily require spending koban. But if you would have missed the rewards without spending koban, it was worth it to spend it.
There are diminishing returns to buying more dojo slots, but it's a reasonable thing to buy. You'll need more inventory slots if you decide you want to equip gear on your defense team, not just your offense team, but you don't really need more inventory slots than you can buy with copper unless and until you decide you want to do that.
After that, summons are probably the best place to spend your spare koban. Platinum x11 or some event summons are the most efficient to buy with koban. But there's absolutely nothing wrong with hoarding koban to make sure that you have what you need for events when an important event shows up. If you're playing completely free and not buying the monthly pass, you're probably not going to have the spare koban for very many koban summons, anyway.
Do not waste koban on shortening cooldowns, buying copper directly, buying the last boat at the port, buying construction tickets, or buying gold summon tickets. Those are all massively wasteful.





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