My daughter had a pro coach for 3 years , she raced at national and international level and was a national champ ( junior) . I did not have a clue what she should be doing so it was far easier to use someone elses brain to tell her what to do. In her case the fees were significantly reduced as she won stuff and therefore gave him a good name. ( same coach as Helen Wyman and 20 other national champs) . Given that she won a lot of races ( regional) I would say they worked for her.
I went on to race myself and hired a coach ( full price) he was a honest chap and yes I improved places and my FTP etc got better but after a year it was apparent I was a sprinter and unless the race was 30 seconds I was sunk. So he re-affirmed what I already knew in that I was not genetically gifted and would only ever be a mediocre racer unless I took to the track. I now just commute to work and race occasionally ( CX) and more recently in lockdown have embarked on a Sufferfest programme, as I have all the gear I can see my FTP has dropped 30 watts from when I last had a coach but I am now 4 yrs older and at 58 its only going to get less. However the programme has already got me 8 watts back so far in 8 weeks.
The experience of having a coach and my daughters experience, is a coach taught me the importance of rest days, tapering for big events and training harder on training days. It also showed me my commutes were not really much of a good training tool,apart from my sprints!
If you are going to race then there can be a difference between a fitness coach and a race coach. The fitness coach is not going to watch you and tell you where you are going wrong in a race , ie being pushed out into the wind, staying too far back, doing too much work etc.
My daughter suffered at national level by not really having a race coach, loitering too near the back and ending up in every crash going, she would not listen to me as I apparently knew sod all.