越來越 climbs one quality against time alone; 越…越… couples two variables — the first must rise to push the second. 越來越好 = better over time; 越走越累 = the more you walk, the more tired.
比 pins one fixed comparison between two things at one moment; 越來越 tracks the same thing rising across many moments.
他的中文越來越好。 (no 了, change unmarked) → 他的中文越來越好了。
天氣越來越冷天。 (noun dragged inside) → 天氣越來越冷了。
他越來越喜歡。 → 他越來越喜歡這裡。 (mental verb still needs its object)
English 'more and more' is one adverb dropped anywhere; 越來越 is a fixed three-syllable block that must sit immediately before the adjective or mental verb, never split.