Yeah, shifters may not necessarily make you go faster - but higher end shifters are lighter, which does impact how much effort you have to do to get the bike moving. And they get rid of a lot of hassle factor.

Race or faster wheels are likely something that will help her a lot now, and she'll probably still need if she gets a new/used bike.

Checking the crank fit might help as well - maybe she needs longer/shorter cranks (could contribute to the leg pains), maybe stiffer or carbon cranks would help a bit.