Will a more powerful amplifier damage the Klipsch RP-600M II?
No — 80 W sits inside the speaker's 25–100 W window, and at 3 m that is 110 dB at the seat. The amplifier that actually kills tweeters is the small one driven into clipping.
No. The 45 W amplifier is the dangerous one.
Klipsch rates the RP-600M II for 25 to 100 W continuous. The RX-V4A makes 80 W into 8 Ω — inside the window — and at 3 m that is 110 dB at the seat. A rating is a thermal limit for continuous power, and music averages 10 to 20 dB below its peaks: at normal listening level an 80 W receiver is delivering well under a watt.
The real failure mode runs the other way. Ask an undersized amplifier for more than it has and it clips. The top of the waveform flattens, and that flattening is high-order harmonic energy — energy at frequencies the crossover sends straight to the tweeter, the driver rated for the smallest share of the system's power. A bass note demanding 60 W from a 45 W amplifier does not simply come out quieter; part of it arrives at the tweeter as treble. That is how «my 45 W amp killed a 100 W speaker» happens, and it is not a paradox.
Practical rule. An amplifier rated above the speaker's maximum is fine as long as you stop turning the knob when the sound hardens — that hardening is the clipping. An amplifier rated below the speaker's minimum is the combination to avoid, because its safe range ends before your listening level does.