The only disadvantage is over working the amplifier. Your speakers will somewhat ask for 60 watts rms when you turn up the volume. However, your amp can only provide 50 watts rms. So if you have the volume turned up more than often you may be making your amplifier work too hard and might burn it out eventually.
Sorry but that just isn't even close to being correct.
The load a speaker places on your amplifier is determined by the impedance rating, not the max RMS power rating. A 4 Ohm speaker rated at 500 Watts RMS will not place any more load on your 50 Watt amp than a 4 Ohm speaker rated for 50 Watts RMS. And a speaker with 60, or 100, or 1000 watt, power handling will not make your 50 Watt amp get a single degree warmer than a 50 Watt speaker, if the impedance is the same.
You're correct about most people these days running amps that are rated at higher output than their speakers are capable of handling. There is some truth to speakers being damaged by over driven amp but that is also something people who sell amps love to say, so they can sell you a more expensive amp.
The fact is that, if you run a quality amp, which is capable of driving the impedance load of your speakers, and set your gains properly, your 60 watt speakers and 50 watt amp will give you great sound for years.