The thing is, the rules encourage you to specialize, and the assumed playstyle does as well. The DM and the players have to make a real effort to make a JOAT character feel equal to the rest of the party. Ultimately, it's a system issue.
IME, this is wildly untrue. I've never put any extra effort into any of the Jacks in my 5e or 4e games, and I didn't need any special effort from my DMs, either. I primarily played Jacks of all trades until a few years ago when I started to really get into more focused archetypes. It fits my ADHD and how I approach life, so it's natural for me to RP those characters.
Being able to help in every single situation, and being able to say, "oh no one else can do that at all? No worries I'm actually rather good at it." in a wide range of situations, is very helpful, and in some systems the Jack facilitates group tactics, making the entire team more effective most of the time.
This gets a bit into how I'd redesign the Ranger, actually, because I think it is a better conceptual fit for the Jack of All Trades than the Bard is.
In a discussion a while ago about rangers, someone claimed that Pass Without Trace makes the Ranger a better scout than the Rogue. I vociferously disagree with that, but it does make the Ranger really good at team stealth, and I think that is an angle that Ranger design should lean into. If you're using journey rules where everyone has a role and makes a check, the Ranger can make their role check
and help another PC with their's. In their favored terrain, it's two other PCs. When climbing, they can go first and if they succeed by 5 or more on an athletic's check, they can give up to X other climbers a +d4. Etc.
Then, give them the actual Jack of All Trades feature, and the ability to grant half proficiency to the whole team on a group check X per day.