Older aircraft were not as sophisticated and maybe needed constant fiddling, but Airbus FBW will climb as efficiently as possible - according to the CI - in CLB with A/THR engaged, and the correct winds entered. Anything else will use more fuel.
Yes, the climb rate will sometimes reduce to a few hundred feet per minute and then gradually recover, but it is working as designed and as efficiently as possible*. In 14 years‘ of flying Airbus FBW, I have only once had ATC query our slow ROC close to cruising altitude.
Soft altitude mode allows the cruise alt to vary +/- 50’ to control small mach variations without changing engine thrust, but soft alt is cancelled by pulling selected speed. Soft alt mode saves fuel and improves passenger comfort. Since changing the CI keeps soft alt mode and adjusts the climb and descent phases as well as the cruise - thereby taking away all the guesswork - I don’t know why some companies forbid it.
*Our Airbus FBW 321’s used about 4 tonnes less fuel to get to Tenerife than our 757’s - different passenger loads, but not that much difference.