You wouldn't go to a dentist for foot pain. So why go to a power lifting coach for sports agility training, or vice versa? ( I know, it's meant to be an exaggeration.)
The fitness industry is massive and overloaded with talent. There's so much to learn and gain with training styles and alternatives in abundance. Somehow this makes reaching your specific fitness goals more difficult, but let's not overthink this!
While on your search for the right trainer, program, or gym, think about YOUR goals and YOUR vision. My specialty and philosophy will be different from the next trainer in most cases. So shop around for what you feel will be a decent fit.
IMO personal trainers need to also be responsible about this and lead by example. YES we are in this professionally, with the goal to get paid for our services and knowledge. We all need to put food on the table. BUT, if you know a potential client has a goal that's outside your profession or a better fit for another training style, be honest with them about it. I've had potential clients reach out for competition lifting style interests. Personally, that's not my style of training so I redirect them to one of my buddies who specialize in Olympic lifting and competition training. There's no shame in knowing your strengths and niche.
Of course we all want to train everyone, but maturing as a trainer, is realizing that some clients aren't always a great fit. Personally, I refuse to run programs I don't believe in.
As a Strength & Conditioning Specialist, who focuses on corrective exercise with a goal to increase mobility and longevity in the quality of my clients life, I can't whole heartedly promote spine compressing olympic lifting that may also weigh heavily on the knees and reduce mobility.
AGAIN, I'm not saying it's not effective or useful, it's just not MY niche. Still, I have the utmost respect for competition lifters for their dedication, ruthlessness, and focus. It's not easy and takes a lot of hard work to achieve the things they do and I will never put down another part of the fitness industry because at the end of the day, we're all trying to reach a common goal one way or another, and help others build up to their goals.