Quite the opposite!!! A mirror is nowhere near as efficient as a cheap off the shelf basic 'polished metal' reflector let alone many of the top of the range reflectors which are often a white metal that looks non reflective!!!
Also a flat panel is not going to reflect light into the tank. Basic refraction (or pool/snooker angles

) can tell you this.
The light leaves the reflector at the same 'reverse' angle it struck the reflector. Same as trying to get out of a 'snooker' on a pool/snooker table.
Therfore the light that goes straight up hits the mirror and then comes straight back down. Problem? It is blocked by the tube on it's return (restrike)
Light that leaves at an angle leaves at the same angle so most of the 'anglesd light is reflected towards the tank glass rather than the substrate.
A top notch reflector will be like a soft 'm' where there is no 'flat' area above the tube itself. light will go up hit an angle and be diverted to another part of the reflector. It may be 1,2,3 ? deflections but most of the light is then guided to hit the substrate rather than being guided outward or back at the tube
However saying that a cheap £5 'curved' reflector like the Juwel/Arcadia ones will be better than using a flat reflective surface as although they will get restrike, they will divert much more light downward than the flat panel will.
Hope this explains it
AC