Remington Steele/Headscratchers

There's an early episode where Steele's old mentor shows up and they plan a con together, not knowing that the mark has already hired the Remington Steele agency on a case. The mark has already seen Steele in another identity, so Laura gets Murphy to be "Remington Steele" for the episode. What bugs me is this: why didn't Laura think of having Murphy play Steele from the beginning, since he's an actual detective and more reliable than the conman? Or even better, if sexism was the reason they weren't getting cases, why didn't they just put Murphy's name on the agency, with the understanding that Laura would still run things?
- Because...where would Pierce Brosnan fit into the show, then?
While the program's ridiculous premise (that no one would hire a woman private investigator) was necessary in the early shows, why bother continuing it after the first season?
- Anybody observing what was happening would be able to determine that Laura was actually the "brains" of the operation and while the mid 80's were less progressive than current times, the thought that a woman could be extremely competent shouldn't have come as a "surprise" to most.
- Yes. The show should have been a period piece set in the 1950s or even earlier. Well, had the show been set in the 1960s it would have still been a decent match, but even in the 70s it wouldn't have really fit the times. And even aside from the "no one would hire a woman private investigator" theme, the show had a noir-ish quality that practically screamed "30s, 40s, or 50s" anyway.
- The premise was even more ridiculous in the first season because the agency had a male private detective, Murphy. He even impersonates Steele in one of the episodes. It would make a lot more sense if she said it was about the money, because surely the name "Remington Steele Detective Agency" attracts more classy, high-profile, high-paying clients than the more down-to-earth "Murphy Michaels Detective Agency" might.