You're right, it should work extremely well. It has for me and I've done nothing special.
I have 5 hubs, each with a Homekit Integration active. I encounter zero Not Responding status, in months. Largely speaking, I can't remember when I last encountered it. Long before Hubitat had the Integration, I only had Homebridge via Dan.T's product and before that the only choice was Tenesto's Homekit package. The Tonesto one (v1?) was fraught with those issues. The Dan.T one was my beginning of a time without Not Responding. Tonesto came out with v2 but I had no reason to try it, so I cannot comment at all.
When Hubitat announced their Integration, because of those initial restrictions, I continued using Homebridge but I did move a tiny number of devices to the Integration to try it out. It worked as well as Homebridge for me, so slowly, I added the Integration to each of my 4 active hubs. They are all connected today, each with a smallish set of devices. 10, 10, 6, 12 is the device count for my 4 "Production Hubs." 8 devices are connected via Homekit Integration from my "Development" hub. Homebridge is down to small numbers as I slowly peck away at the device list: 17 devices. So that's 46 devices using Hubitat Homekit Integration and 17 using Homebridge. I only select Actuator devices. I do not select Sensor devices. Yes, some Actuators have a sensor too so Homekit sees both, but my intent is to onlyhave devices on Apple that I might want to control.
I've tried to figure out how my situation can be so stable, yet others say variations of "it hardly ever works". There are only two factors I can think of, and neither seem shattering 
First, I've been attempting to use HomeKit for 5+ years. It's gone from unstable to stable over that time. The two biggest events are, the Hombridge rewrite by Dan.T and Apple's big update (IOS v16.4 in 2023). Second, I have what I consider a tiny number of devices per hub. Others, with a single hub can't do that obviously. I have no idea if there's any validity to this one because Homebridge was fully stable for me, long before Hubitat released their HomeKit Integration and I had everything going through that one path.
All 5 of my hubs were rebooted about 19 hours ago to the latest platform across a 2 hour period. In other words, I've had 5 opportunities to experience what you experience in the past day. I never had any sign of a problem and when I've looked, while typing this message, all 5 hubs and Homebridge are communicating perfectly.
But again, it should be working well for you, just like it does for me.. you are correct in asking for ideas. Sorry I have none. 
