It goes back and forth on the idea of having cows that are TH and PHA carriers. Really depends on who you talk to. PHA is much less common (at least in the club calves, influential Maine sires like Whiskey was a PHA carrier), but is also more deadly. PHA on PHA breeding can usually result in a dead cow and calf if not monitored extremely close.
TH is found in almost all clubby bloodlines today, because most of those bloodlines go back to Heat Seeker, who was a TH carrier. There was obviously some TH negative offspring from these matings, but notable offspring (at least sires) are normally carriers- Heat Wave, Monopoly, Man Among Boys, Unstoppable, etc. This is where it will begin to depend on personal opinion on whether or not those females should be retained. Some people love daughters out of above said bulls because they often make great steer mommas. They will normally take the clean cows and breed them to carrier bulls, and often the carrier cows will be bred to a carrier bull. Others prefer more maternal bred clean cows to then use the above said bulls on. Whether or not your cows are the type to be more prone to carrying the lethal TH defect will completely depend on what your idea of a good, producing cow is- a stout one that looks like a steer, or a more maternal based cow.
It has been argued that TH carrying animals possess more bone, hair, and overall have more of a "steery look" to them. While this is most likely true and quite frankly I believe in the rule of thumb, I don't know of any studies conducted to compare negative to positive animals.
I think the root of the TH problem can be accredited to the changing desire of female cattle in the show ring. More often than not, your composites, chis, and percentage cattle are winning the heifer shows. Most of the time, these calves are sired by terminal, TH carrying sires. Most owners believe that these cows will later on be good producers and will breed them instead of shipping them. Again, this a matter of personal opinion on what you like to see in a cow. Personally, I believe that a good half of your composites, chis, and some composite animals should be shown as market orientated animals and not be bred and used for production. Again, personal opinion.
I know I didn't address PHA but I have minimal experience with it and I'm sure so done would be able to chime in on that topic.