I wouldn't suggest getting into the habit of binding simply because it can cause tissue damage over time. Personally I never have problem with underboob sweat- remember that though it may seem counter intuitive, you should be pushing them /up/, not down, when you bind, or you're going to risk some serious damage. I'm a D cup and I can bind completely flat this way. Tissue damage isn't really as much of a problem if you're considering top surgery sometime in the future, but since you're agender I'd guess you probably aren't.
Sports bras can also actually flatten things quite a bit. Some people use two, or use sports bras in combination with other binding methods.
Also if this is any help to you, here is a really quick cheap and easy binding method I sometimes use. It's not a long term solution as the hose break down over time, but you can try it out and see what it's like having binding as part of your everyday routine before investing in a binder top.
