Actually, your problem raises interesting questions. Normally a router is supposed to be always power on in order to listen to broadcast commands that affects the network. I will not go into details, but, under certain circumstances, it seems possible that a router will not be able to rejoin the network if it has been down for some times. Furthermore, it does not seems that the behavior of a router when it restarts is fully defined (e.g. rejoin command not mandatory). So different brand will behave differently.
However your setup is quite common particularly for bulb lights. Personally, I will put some switches on the bulb lines so that if the home automation system is down I can at least turn on my lights.
Philips is definitively a major player in Zigbee and it making very good products, but that does not mean that it provides 100% Zigbee compliant devices. For example, according to @MattWestb some old Philips bulbs (but not so old) do not implement neighbor aging algorithm correctly. Therefore, you can be left with long time gone devices still reported by the router.
You may be tempted to keep Philips devices all grouped under a Hue hub and the rest of your Zigbee devices connected to the ConBee. This will work but by doing so you are removing many routers from your network which seems a bad idea as it seems that the more routers you have the more robust your network is (especially to interference).
I just power down few hours ago one of my Hue bulb router with an Aqara end device directly connected to it. I will wait until tomorrow to see what is the behavior of the bulb when I turn it back on. Normally it is possible to specify the behavior of the bulb when the power comes back (on, off, same state). This is easy with the Hue application but hard with ZHA.
One thing I do not like in HA is the fact that when a Zigbee device is gone (or down) there does not seem to be any indication in HA. For the Philips bulb (down) if I try to turn on the bulb with an HA button after a few seconds the button goes back to off state without any indication (error message). I suppose the command is sent but obviously not received by the device and HA must try to read the status back and not receive anything. In such a case, it would be nice to “grey” the device to indicate that it can’t be reached. oops it works as it should - just have to wait that it gets detected as not available
Note that the Zigbee graphs (default visualization or Zigzag) do not reflect the fact that the device is off. This kind of make sense as the graphs are updated every 3-4 hours and furthermore the device is probably still in the neighbor tables but it would be nice to get “real time” information. Even zha-network-card display the device as “online = true”?