I think YRMW was the right choice.
You've got to remember in 2001 Mike had been out of the spotlight for years (at least on the big stage) and his last few singles had been more serious or more angry topics (understandably) So YRMW was not only a shock but it was a much needed breath of fresh air.
The problem with looking back retrospectively is you lose context. YRMW single/Invincible release was probably my earliest memory of Mike, you couldn't get away from the song, it was either on the radio or it was coming up next. For about two months it was everywhere.
The only thing that stopped YRMW going to number 1 in the UK, was how massive Can't Get You Out Of My Head by Kylie was. That song was on all time and the video was played constantly.
YRMW should have been an easy UK number 1 single - it sold 93,000 copies in its first week which was considerably more than the median average of a UK number 1 single in 2001.
Now, you are right, one issue was that Kylie Minogue was having a once in a lifetime critical and commercial smash with CGYOOMH and that happened to be competitor for YRMW.
However, there were other issues at play.
1) YRMW was released only on one format (typically, in 2001, UK singles were released on two CD formats to boast sales).
2) YRMW had no notable bonus content (e.g remixes).
3) YRMW retailed at a full price of £3.99 (typically, in 2001, UK singles retailed at £1.99 for its opening week and then £2.99 or £3.99 afterwards - YRMW almost uniquely was not discounted to retailers at all).
If any of the above three factors were different, YRMW would surely have sold the few extra thousand copies to debut at number 1 and overtake Kylie.
I have explained elsewhere I was partially engaged with the UK/European marketing campaign for Invincible and already have given reasons why there were no remixes, which explains the 1st and 2nd issue. These were issues out of the UK label’s hands.
As for the third issue. Yes, I understand it probably stopped YRMW from hitting number 1, but objectively speaking it was no doubt the correct decision from a financial/profit view.
Either way, YRMW was huge on UK radio and did what it was meant to do.