Let's not get too carried away with the theory that lack of power kills tweeters (or any driver). Drivers fail when they are exposed to more wattage than rated for longer than their materials can sustain it, or because of material failures within the rated power range due to age or because the design is flawed. Although you can increase the total amount of wattage the tweeter is exposed to by clipping the signal, you can't increase it beyond the theoretical wattage produced by rail voltage of the amplifier driving it. However, if you are using an amp close to the speaker's rated power and you clip that, you will definitely exceed the wattage the speaker was designed to handle.
The systems that the 044 were used in are all in the 300 WRMS power handling range. This tweeter dissipates heat reasonably effectively and in my experience is pretty robust. If it has a weak point, it's the lead wires where they cross the gap between the frame and the voice coil. You can cook that if you work at it a little bit, but worrying about doing it with a 60 watt receiver is silly.
FWIW, I own & use regularly L96, L112, L150A systems. The 150A's are running off a pair of bridged Sony TA-N55ES amps at 300 watts per speaker. The other pairs are generally run from either a 75WPC Tandberg TR 2080, or the 85PWC from my Sansui AU-717. I've also used them on a single TA-N55ES which is about 110WPC in 8 ohm stereo.
In 5 years, I've only lost one 044 tweeter. I actually fixed it (it burned in the gap between the coil and the frame where I could solder a jumper) and continued to use it afterwards. This happened back when I first bought the L150A's and was running them in my big system, cranked up hard with the 300 watt Sony amps driving them. My guess is that tweeter was already partially damaged and I just finished it off. I haven't had a repeat of that, and I still drive them hard regularly. I did replace that tweeter later with an undamaged one though.
Just my $0.02...
John