Have you looked today if you have an un-opened PM ?.
No, but if I had one it shows this in the header, discreetly. Just like almost every other forum I participate in.
If messages are important then, just like every other forum I've seen, there's an option to be notified by email.
Fit for purpose in my view, with no need to change. 8)
PS If I want people to communicate with me with some urgency I give them my phone number or email address.
A message on a forum, from someone I have NOT chosen to give either of those, is by definition going to be dealt with as and when it suits me.
I have no greater expection in relation to forum messages I send.