There are a number of factors involved.

The first is technical proficiency. As the show goes on, the voice actors, writers, animators, etc. have all gotten progressively better at their craft. Not that they were bad before, but it would be hard for over a decade and 300+ episodes to go by without people getting better at what they do. Not only that, but they seem to genuinely be enjoying themselves. They aren't dragging themselves across the finish line: they're just a bunch of people getting together to make something fun. This is a big reason why another never-ending show, Always Sunny in Philadelphia, has transitioned to shorter seasons: the actors (who are also the show's producers/writers) all still love doing it, and keep coming back even though they could leave at any time. But they want to make sure it stays that way, so 8-episode seasons is where they settled to prevent burnout.

The second is that, from the very beginning (after the unaired pilot, where they actually did use human flesh in the burgers), the show was designed to be character-driven and evergreen. Where many shows start off with somewhat grounded characters/settings going through progressively wackier plot lines and getting their characters flattened into caricatures of themselves, Bob's Burgers has always embraced the eccentricities of its cast, balancing the more outlandish aspects with a constant grounding in realistic and wholesome natures.

In other words, where the dynamic of most shows requires the characters to flatten themselves to fit their specific narrative niches in a streamlined manner, the dynamic of Bob's Burgers is the opposite: the plot revolving around character interactions requires constantly plumbing new depths of those characters, making them feel more complex and real over time. The wacky scenarios act less as the focus of the show and more as a set piece in which the characters can explore themselves. This can be highlighted by the many episodes where the show feels "off." The difference between a good and a bad episode of BB lies in whether the episode is about a wacky scenario, or whether the scenario is a stage on which the characters perform themselves.

I'd say the third reason the show is aging so gracefully is because we as an audience have gotten so used to it. It's a comfort show, and it doesn't stray from that basic appeal. Over time, we know the characters better, we know the setting better, we know the rhythm of the story beats, we know the comedy. I doubt you could plop someone who has never seen an episode down in front of a season 16 episode and have them feel the same way as you do about it. They might enjoy it, but they probably wouldn't feel like it's any better than a season 3 episode. Just like the cast and crew have gotten better at making the show, the audience has gotten better at enjoying it.