[...]
By using google found this converter
https://html2bbcode.ru/converter/ but don't expect it will convert every html tags, coz making good-looking signatures is somewhat difficult for signature non-designers ofc.
After reading about bbcodes it seems they have already classified different styles of BB code. I mean one conversion site shows options like:
HTML to BBCODE
HTML to SMF (Simple Machine Forum) _____ [believe we use this one]
HTML to vB Code
HTML to IPB Code.
Site does show that while converting HTML to specific BB type will have output options like [code, [php], [xml] and multiple options too.
We will loose the <textarea> in the process or it remains unchanged. So I suspect if there are links in the bbcode they would go out of the signature space.
Same case with the order of list.
Since BitcoinTalk is based on SMF Bulletin code we have PHP and Code options. The article is interesting but not that clear, still they have managed to make this converter.
But as @bL4nKcode said, it would be a real mess.
**In my opinion We are just doing fine with the current methodology.