So lately I'd been trying to parse the subtleties of proper use for some of the lesser particles and a lot of effort has been spent on how to get 'po' to properly get into the semantic flow of a sentence instead of the clause-handbrake it often throws up. So after some considerable time searching for various precedents and making comparisons in the PMEG, it basically comes down to whether or not the 'idiomatic' usage is as grammatically valid as the 'classical' syntax, which starting from a base sentence of say:

You should drink at least one glass of tea a day.
Which ideally I guess should be something like
Vi devus trinki almenaŭ po unu glason da teo ĉiutage.

Which however runs into some semantic problems by putting the 'po' between 'almenaŭ' and the thing it's supposed to qualify, which now seems closer instead to something like 'the least you could do is drink one a day'; and even though word order is more dependent with distributives, because the quantities would still be the same if it's a 1:1 equivalency it would be easier to reduce ambiguity by moving it to:

Vi devus trinki almenaŭ unu teon en po unu tago.

In this case it's a matter of point to emphasize the unu for teo as a stated non-zero minimum, but is not especially necessary for tago except for that 'po' must apparently always be followed by an expression of quantity. But could it not also be possible to drop a number when it's synonymous with a singular indefinite? And considering also that: "La akuzativo povas anstataŭi prepozicio por montri tempon / ekz. en ĉiu tago = ĉiun tagon" it should be possible to excise enough to simplify it down to:

Vi trinku almenaŭ unu teon po tagon.

And then to disambiguate the two direct objects, why not further reduce it to its essential meaning:

Almenaŭ unu po tagon

So is this too far gone to be comprehensible? Because given how frequently words are elided in idiomatic speech and phrases, I see no reason for it not to comport with the same principles that gave us 'bonan nokton'.

Laŭ mia Retaj serĉoj, ŝajnas ke oni diras kaj po almenaŭ kaj almenaŭ po.

Do por via taga konsumo diru laŭ via plaĉo almenaŭ po unu tason aŭ po almenaŭ unu tason.

La lasta imitas la ŝablonon de Ĉiumonate tage ili ricevis po ĉirkau ses mil dolarojn.

how do you begin a new forum, sorry.

Hopefully I'm not missing the point, but "po" is just a preposition like any other with a specific distributive meaning that parallels the suffix -op. It's often not immediately clear to some speakers whose language lacks that word. It doesn't strike me as a flaw with "po". Sudanglo covered the adverb issue.

Though "po" can sometimes be done away with by a word like "tage" or "ĉiun tagon", sometimes it really is the most elegant solution: Ni trinkis po du bierojn. Li pagis al mi kaj mia frato po 5 dolarojn por la laboro.

ni tri trinkis po du kafojn (entute: ses kafoj trinkitaj)
ni kvar venis kun po 3 amikoj (entute: 12 homoj venis)

ili du pagis al ni tri po kvar dolarojn (kiomaj dolaroj???)

miksu tri partoj de viando kun ses partoj de faruno kaj dek partoj de akvo
miksu laŭpese viandon po tri, farunon po ses, akvon po dek