Debbugs works great for being last updated 12 years ago. It's main interface is email, after all, so the web interface is read-only. I think the real issue here is the hardware it's running on.
The reality we live in today is one in which traffic spikes come without warning, whether from sudden media attention or DDoS. One of the core features of the web is the ability to link to web sites. If a service can't handle traffic, it shouldn't be accessible from the open Internet, least of all if it's a service run by a major Linux distribution.
Classical Linux userland devs (I count myself among them) had a tradition of dissing web development as "not real software development". I also do web development, and it seems Debian could benefit from ditching that mentality and encouraging a volunteer (or using some well-spent funds) to make their bug tracker safe for the 2016 web. All it probably needs is a caching proxy.