True, vinyl numbering has it's place and is fast, easy and clean.
Direct printing was a requirement for the numbering projects we did for a couple of large Portland "shoe companies". The perceived quality (whether correct or not) was higher for direct printed numbers.
There still seems to be a stigma attached to vinyl numbering in regards to "peeling off". I know that issues like that have largely disappeared, but we still get asked about it when we mention heat pressing to clients. It's kind of like the old "does the ink get all cracked after awhile?" question.
In regards to waterbase printing of numbers, I'd have to say that I'm not sure it would work well, especially on the fabrics you mentioned. Straight waterbased inks lack the opacity needed for printing on dark. On dark garments you'd generally use discharge ink for waterbase. The fabrics you mentioned won't discharge properly. Not to mention that discharge inks historically have not been very "environmentally friendly". Especially in some shops where they think that since it is waterbased it can get rinsed down the drain. Unfortunately, some shops do this with regular waterbased inks as well.
Unless you have another reason to use waterbased besides environmental I would look at some of the new plastisol inks. There are some offered now that have removed most (if not all) harmful chemicals. In fact the "shoe companies" out here require the use of such inks.