I was going to say that I wouldn't argue with Cream being the first (at least with all members having equal billing), but then I remembered The Who, debuting two years before Cream. Does having a fourth non-instrument playing member disqualify them as a power trio? There are examples of the power trio sound before Cream but with the guitarist as the acts name, not a group name. American guitarist Link Wray (whose sound was that of a trio) is acknowledged by Pete Townshend, Jeff Beck, and Jimmie Page (as well as other Brits) as being an inspiration to pick up a guitar. But Link was part of the "Rock 'n' Roll" generation (the 50's), not the "Rock" one (the 60's), if one wants to differentiate between the two terms and eras.
It was the power trio style of Cream that Clapton wanted to distance himself from after hearing The Band. Power trios, where all three instruments vie for equal frontline status, became known amongst certain kinds of musicians (like good ones ;-) as embarrassments, being comprised of "lead" bass players and "lead" drummers, not referred to as such as a compliment. The art of playing a supportive role (remember rhythm guitar? The power trio made it uncool to not be a "lead" guitarist. John Lennon was an excellent rhythm guitarist) was lost for a while, until The Band emerged from the basement of Big Pink to save Rock 'n' Roll.
On a separate note (no pun intended!), the internal bickering in Cream was well known, and assumed to be between Clapton and Bruce, since they were the frontmen, and had to split the lead vocal glory (though Bruce was really their lead singer, wouldn't you say?) and songwriting royalties. But it was actually between Bruce and Baker, who couldn't stand each other.