Learn English – Origins of the phrasal verb “to fall asleep”.

There are relevant sections in 'Multi-Word Verbs in Early Modern English: A Corpus-Based Study' by Claudia Claridge, précised at http://linguistlist.org/issues/12/12-698.html which contains:

Chapter 5 examines the history of these types of multi-word verbs from Old English through to Modern English. ...Chapters 6 and 7 describe the particular multi- word verbs found in the Lampeter corpus, and attempt to describe the patterns found among them. Chapter 6 treats the data synchronically, while chapter 7 looks at diachronic developments during the 100 year period covered by the corpus.

I've accessed various portions online, but had to order a copy via my local central library.

In an article by Catherine Browman at http://web.haskins.yale.edu/Reprints/HL0594.pdf , it is stated that the transformational grammarians Absalom (1973), Chomsky (1957) and Fillmore (1965) considered the contiguous form to be basic and the separated form a movement-transformation derivative, whilst Edmonds (1972) believed it was the other way round. Other grammarians, such as Gazdar, Klein, Pullum and Sag (1985) retain the verb and particle as separate constituents, but seem neutral with regard to direction of transformation (if any).

(Still other grammarians regard the verb-particle combination as more or less unanalysable, in any given example.)

From John Dryden's 1700 Palamon and Arcite (a translation of The Knight's Tale from Chaucer's Canterbury Tales)...

So thou, if fortune will thy suit advance,
Love on, nor envy me my equal chance

Two guys both fancy the same girl; less poetically, the speaker is saying they both have the right to try their luck and love on (i.e. - continue to "love").

My guess is Dryden's love = pursue your suit (archaically, make love to her). But you could just as easily interpret it as experience feelings of love for her. The point is there have always been contexts where (verb) love can be followed by on.

But I don't think there will be any "acceptable" instances of (verb) love on [object of love], in the sense of being considered "grammatical" by any significant proportion of Anglophones.

OP's two instances aren't really the same. The first [mistakenly] substitutes on for towards (AmE toward), probably echoing preceding in the streets. The second is just a quirky "slogan" format.