Forum signatures and other low quality backlinks are like dust to me. Dust is not necessarily bad. Every house has a bit of dust in it and that is ok. The problems start when you try to build your house on a foundation of dust instead of a firm foundation.
Forum links are part of SEO strategies and have very, very high value if well done.
Some of my sites rank top 5 in my industry by being an active member of a dofollow forum with PR9, hundreds of posts. It is almost enough to single handedly rank me...and no, not from that forum, from Google.
It's a fact that link portfolio and diversity is crucial in this day and age after penguin.
So limiting the ammount of same anchor text is a punishable red flag.
Your opening question is built on a premise that many here feel to be false these days. So any answer, either yes or no, is like reinforcing an old or outdated model of SEO.
Assuming that forum signatures still have value (and I don't) I would not suggest using an anchor text signature. I like your idea of just the domain name. Even with the best posting history, there's not much reason to use anchor text except blatant, old school SEO. Even if it currently seems to work (which I find unlikely beyond a certain minimal threshold) I would expect it not to work very well into the future.
I doubt that the anchor text itself is all that unbalancing if we're talking about one forum, with real involvement and consistency across posts rather than hundreds of keywords. That kind of firum sig, where permitted, is not the same as strategic involvement in many forums for the purpose of getting backlinks. That's something Google can detect (it has a very fat, screaming footprint) and at the very least is devalued.
The key for all backlinks is natural diversity. One forum with one standard sig is no big deal - but that can't be a major part of the natural diversity you need to move the needle at Google. And there's little reason to think that involvement in a pile of forums is real in any way at all.