The problem with sweep tubes is they were designed to handle enormous excursions outside the normal operating range. For example, most can handle peak cathode currents in excess of 2 amps and hold back over 6000 volts on the plate without arcing! This was required in older TV applications because at certain parts during the electron beam scan, the operating conditions can approach these levels but only for a very brief instant and extremely low duty cycle.
In linear applications this translates into a false perception that these tubes can make much more power than they can actually do comfortably. Some time ago I observed a RM amplifier with one EL-509 driving another EL-509. The amp could put out a 500 watt carrier but would trash the output tube quickly if you got long winded. Just because they were designed to take this abuse for short durations certainly does not mean they can handle it for any length of time.
It all comes down to the dissipation the internal tube elements can handle continuously. The 2 amps or 6000 volts are specs that are allowed for tiny fractions of a second and do not occur simultaneously. The EL-509 can make 500 watts but it has a plate dissipation under 40 watts so it dies very fast.
Tube life is not proportional to output power once you exceed the specifications. I've seen sweep tubes run close to specs that provided up to 2 hours of use per day for about 10 years. If you drive the amp hard to make twice the output, the tubes won't last 5 years, they may last 5 weeks if you're lucky. You'll either strip the cathode of its oxide coatings or melt the internal elements of the tube.