What is the intended use of high current SSRs and triacs?
Yes, they are used for high power switching, and not necessarily at a low duty cycle.  I run hundreds of SSR's anywhere from 5A/240VAC up to 100A/460VAC/3P.  Past 100A, it is more common to use back to back SCR's and a small firing circuit (and large heat sink).

The typical application is for resistance heat control.  Contactors/Relays are not a serious option, because of contact wear (the typical 'duty cycle' is 2.5 sec on/2.5 sec off). 

Basically, a timer is free running for a certain period (I use 5 seconds mostly).  The heater is switched on and off for some period out of that 5 seconds to control temperature, based on the output of a PID loop.  10% output is on for 0.5 sec, off for 4.5.  90% output is on for 4.5, off for 0.5.  Those duty cycles kill electromechanical devices quickly.

There are also hybrids, that use a relatively small SCR to turn on a load, then close an electromechanical contact around it (to prevent closure arcing), and then the SCR is turned on again when opening the contacts.  Those are pretty special purpose though, and expensive.

Mercury Whetted relays used to be used, which didn't have the contact wear problem, but in the past 15 to 20 years, industry has been trying to eliminate them due to the problems of dealing with heavy metal contamination, and disposal.