I’m sorry, blue. I’m not clear on what you’re saying. You are talking about the “email address”, not the “email messages”, right? Also, not sure what you mean by not requiring a password… I’ll try to explain a bit more clearly.
When you use Formspree, you have to tell them which email address to forward the messages to by putting it in the form’s action. This means that, as you point out, anyone can find out what that email address is. There are bots that scrape for email addresses in the html of websites automatically. If it’s not a bot, a person could get it by looking at the source code or inspect. Because of this, I think the risk for getting a lot of spam in the future is high. That’s why I suggest using a temporary, disposable email address that you will ONLY use for this purpose.
You can create a new email address with yahoo, microsoft or google very quickly and easily. If, in the future, you start to get too much spam, you can stop using that email address and make a new one. That’s what I mean when I say it’s disposable and temporary. You will probably not keep using that email address for a very long time.
When you create a new email address with one of those services, you are always required to make a password. I have never once seen a service that lets you create an email address without a password. Of course, only you know that password. You don’t put that password anywhere in your HTML.
So if you create "email@example.com", for example, you will also need to create a password, say “bluepass”, which you will keep private. When a user goes to your site and sends you a message, Formspree forwards that message to your "firstname.lastname@example.org" account. For you to see that email, you’ll need to login to your email account using your password.