Super Sentai has always been anime-like. It's just that what type of anime Super Sentai is emulating changes over the decades as anime evolves.
Super Sentai of the 80's was heavily patterned after the types of anime shows, particularly Super Robot mecha shows, Toei Animation made in the 70's. Competing studio Sunrise pretty much killed this approach to anime with the release of Gundam in 1979, so in many ways 80s Super Sentai is where Toei's Super Robots lived on. Toei's Super Robot work in the 70s had a lot of creative vitality and enthusiasm that I feel is directly continued by the Super Sentai of the 80's. 70s mecha shows had a tendency to be surprisingly grim, too, a quality 80s Super Sentai also retained. Basically Flashman is I feel a show Tadao Nagahama inevitably would've made if we hadn't lost him to a car crash.
In the 90s you see Super Sentai leaping over a decade of anime evolution to be written more in the style of then-contemporary anime. The trend toward surreal comedy you see in the early 90s shows like Dairanger was also ongoing in the most broadly popular comedy anime. Megaranger was consciously patterned off of Toei Animation's then-ongoing major hit Sailor Moon, which was itself an attempt to fuse magical girls with the tone and feel of Super Sentai in the 80s. While the stories are lighter, you see more elaborate plots crop up in the best Super Sentai of the 90s because anime was trending toward tighter, more elaborate plotting.
What Black Fang calls "anime-fying" in the 00s just reflects the way anime transformed at the turn of the century (generally for the worse, IMO, but I'm old and bitter). The most broadly popular shows became much more abjectly comedic-- in fact most of the really breakout new properties of the last decade are comedies or romantic comedies. The rush of tons of power animals reflected a trend toward dramatically increasing the number of toys that toy-selling anime like Digimon-- another Toei property-- had to be able to support for a franchise to be successful.