Nozzle insulation gone, can the printer be damaged?
Removing the insulation will not damage the printer, although it may affect the quality of the prints. The insulation is, after all, there for a purpose.
Allowing too much heat to escape radiatively from the heater block will reduce the maximum flow rate, since less energy will be available to heat the filament, and you may need to reduce your printing speeds or increase your nozzle temperature.
A bigger problem is that heat radiating from the heater block can cause already extruded filament to sag, especially when printing details and intricate infill. If the nozzle remains too long in any area, already extruded filament is likely to soften and deform. Without adequate insulation, the only way to counteract this is by increasing part cooling, and this will remove even more energy from the heater block.
Either fit new insulating tape or buy some silicone socks, since they are readily available for MK7/8/9 heater blocks. Then print a couple of Benchies, both with and without a sock, and compare the results.
There is not less energy available unless the block is excessively cooled by the part cooler. The thermistor will read the temperature, when it drops below a certain temperature the heater will heat up. It also does that with the insulation on. It is expected that the heater will be scheduled more without insulation.
@0scar You're right. I was speaking too much from personal experience. I'll edit my answer.
Thank you, I'll look into silicon socks. According to what I read it's thermal conductivity is far higher than that of the former insulation material but it'll still be better than just air, and it'll avoir PLA buildup around the nozzle which is basically what destroyed the insulation band.