Yep, when I was a financial advisor years ago, this was a point of emphasis with clients, especially those with a high volume of trading activity. If you don't know what you're doing and don't plan well, stuff like this example can easily happen.
I just got through what was a seven-year process of selling a company and each year had installments that were capital gains, generating significant tax (the company was long-held so the basis was zero). After the first year or two of trying to bank the proceeds and earn some interest until tax time, it was just too hard to avoid co-mingling the funds and then you get in the spot of having a big tax bill. So I started just sending in the tax payment at the time of receiving the money.
It's far easier to just send the money in at the time of the gain (you're supposed to anyway). Frequent trading doesn't quite lend itself to that (there's a bunch of events, not just one or a few) - but traders should definitely be sending quarterly tax payments to avoid this problem and be more disciplined about it.