Yeah, having no gcd heals really wouldn't change much in high level play; everything is planned out as is after all.

It'd just make dungeons take forever as people wait for healing cooldowns to reset before pulling bosses. It'd also make casuals just not want to play anymore, since mistakes are much more punishing for healers and non healers alike.

It's just one of the many quirks of healer design in FFXIV.