It seems like wording is contagious, everyone keeps telling you to "remove" the heat lamp even after you've said it's a permanent fixture. Which is fine, just turn it off, provided they are fully feathered. EOs can be slow to fully feather, so check their backs for any bare spots.
And you're right about the security of the fixture being one of the dangers of heat lamps. But so is flammable dander... chickens release a lot and it all seems to cling on to the lamp housing. And age of the bulb is another danger. Any hotspots or points of weakness in the bulb can lead to an explosion which rains flaming debris down into the bedding... and that is the way people's barns / coops burn down.
Though, it's my belief that heat lamps can be made safer!
One way would be to use fine (1/4 inch) hardware cloth made into a dome underneath the light fixture (well away from the bulb) that would catch any exploded shards. That would work best with metal sheet flashing covering the wooden / plastic surfaces in the vicinity of a light.
But in any case, the keys to using heat lamps as safely as possible is to dust them before every batch of chicks. Never touch the bulbs (skin oil creates hot spots), or place them where water could be flicked onto them.
Change the bulbs out at the slightest sign of failure (flickering) or discoloration. Secure them well (as you have), and ensure the electrical connections are safe and of an appropriate gauge, etc.
I'd listen to
@rosemarythyme about the ventilation. It's important to keep humidity low in the coop, and chickens release a lot of vapor from their breath, not to mention the water source you mentioned keeping in the coop. Those two little port vents are not going to release enough humid air to keep them dry and comfy.