Most simple unmagaed PoE switches don't support LLDP either.
In a fully managed PoE switch the switch will track power budget and allocate power according to what the devices report. A PoE device will full implementation can say "I'm a Class III device, but I only need a max of 13 Watts, not 15.4" and the switch can then reserve 13 watts of the power budget for that device. If the device only reports it's class, then the switch would reserve a full 15.4 watts.
In simple PoE switches there is no power budgeting at all. Your switch/power supply has a max output wattage, and power is just allocated up to the limit based on total draw at a given moment.
Neither scenario will cause the power supply to push more power to the device causing wasted power in the sense of increasing your electrical consumption.
In most cases the cost delta between a managed switch that supports full LLDP and power budgeting and a cheap switch is large enough that it's not really worth buying the more expensive switch just to be able to put an extra device on it.