No need to move your post - we maple people are general tree people as well:-) We just like maples a lot! And the answer to your question is pretty simple. The anthracnose will be an ongoing problem if conditions exist for its development and regular, at least annual, treatments will be required to control it. It is seldom a fatal affliction but it can cause defoliation and that can weaken the tree, leading to other issues. Plus, a tree with anthracnose always looks pretty funky and unhealthy. The pathogen that causes sycamore anthracnose is unique to that species so composting the diseased leaves should not pose any problems unless lots of other sycamores in the vicinity and the composting process not very thorough. Although a diseased sycamore will not grow as fast or as large as a perfectly healthy tree, they can get quite large and maybe not the best choice for a suburban garden. I'd look into replacing the tree with something that will be more attuned to your specific climate and location, like a native Texas species or something like a Shantung maple, Acer truncatum, which is very well adapted to a TX planting situation.

That's what I'm thinking: hickories and a walnut. Definitely Juglans for the last one at any rate. One like a butternut or Asian walnut.

Yup, agreed on the ID. You could probably take cuttings a few nodes long & pot them back into mother plant's pot, to make it look even more full & lush.

Foliage-wise these do not look much like suckers from any stock I have seen used here. They do look like Japanese cherry seedlings - something I have seen numbers of coming up on more than one local site (where seed source trees were fully visible nearby). Try pulling a small one up and seeing if it pops out with its own small branching root system or if it turns out to be coming from a large horizontal root. One that leads back to a much larger source tree in the immediate vicinity.