Hi, Neil. We use both approaches where I work. Often, a hybrid of both in one banner. Some kinds of complex animation, like cartoony things or animated masks, really need a timeline to build efficiently.
We recently did a series that used Animate for a logo animation in a canvas tag, but the rest of the banner was html with GSAP.
One shortcut in hand-coded banners is to keep all your image files the full dimension of the banner. So if you're building a 300x250, you end up with a stack of divs holding 600x500 transparent pngs, scaled to 300x250 for crispness on high density displays.
Without Animate, type is usually done as images. The advantages of web fonts don't apply so much to ad banners. We don't care much about SEO, copy and paste functionality, accessibility or responsiveness in an ad banner with fixed dimensions. A web font isn't worth the file size and trouble, unless you need dynamic type, in which case you need to look into font subsetting and hope you can use web fonts.
I don't think you need an app for your banners, just a text editor, some patience, and some examples to look at. Try Google's 728x90 here: https://support.google.com/dcm/answer/3145300?hl=en - good luck!