It's problematic for a company if they have to announce their EOL plans on product announcement to get interest from customers. Might as well not exist as a company at that point
It's problematic for a company to have EOL plans not because people will assume they will go out of business, but because they might not be able to actually adhere to those EOL plans resulting in a much larger mess than what would have happened if they stayed silent.
It's bad, but I'm not sure it's that bad. In B2B land, loads of contracts have a code-in-escrow clause just in case key people die or the company goes under. One of the key attractions of Open Source is that if the people building it die or don't want to support the tool anymore, you can keep going yourself.