Can Americans with a Charles Schwab account transfer money directly to a Thai bank without using a service like Wise?

You can easily, but you will pay dearly for it.

With increased scrutiny from USA banks on offshore activity, expect to run into some issues when you declare your Thai address

The benefit of the Schwab account is the refund of the ATM Fees. If you have a Schwab account and you want baht, you should be getting it from the ATM in Thailand. And you should always get the maximum amount possible. Each brand of ATM has a limit on how many bills they will dispense, some are 20, some are 25, some are 30. So that equals to a maximum of 20,000 or 25,000 or 30,000 baht depending on the bank ATM that you choose.

If you were going to transfer money from a bank to a Thai bank account, there's not really any benefit of doing a direct bank transfer because you're never going to be exactly sure how much you are going to receive between possible outgoing fee, conversion rate, and incoming fee which is usually a % of the transfer. Wise is better because you'll know the exact fees and the exact amount of money you're receiving into your Thai bank acccount.