I have heard it said that 5e does not balance its encounters with respect to magic items; in other words it does not consider possession of magic items when defining appropriately challenging encounters. But what about mundane items? Specifically, plate mail. Due to its cost, it stands out dramatically from other, mundane items.

I have read numerous forum posts discussing the "correct" rarity of such an item, and what character levels are fitting for PCs acquiring it. What troubles me about this is plate is a significant part of the Heavy Armor proficiency - if plate (and to a lesser extent, splint) is not available (either by gold restrictions or the DM saying it's hard to find) then Heavy Armor proficiency becomes much less valuable to a PC. Light Armor users easily get to 16 AC, and Medium Armor users can get to 17 at half of the cost of plate. Now, plate is 18 AC, but it comes at a great financial cost, Strength restrictions, and Stealth disadvantage. Seemingly, the only real benefit is that they can also get to 17 AC cheaper/more easily than any other armor proficiency.

Still, in many campaigns plate is out of reach for the first five (or more) levels, making the Heavy Armor proficiency relatively weak for any classes that offer it. Even once that point is reached, AC tends to be less important than raw HP or magic resistance/saves at later levels - so by the time plate becomes available, it matters less than it would have earlier.

In short, I identify that the availability of plate mail as a huge "swing factor" in the value of Heavy Armor proficiency.

Do any 5e official sources (source books, designer statements, or Adventurer's League) offer any indication on the appropriate time to allow PCs to have plate?

RAW: Somewhere between levels 5 and 11

Six levels is a lot of variance, so let's see what we can discern. Looking over the expected results from the treasure tables in chapter 7 of the dmg and the "starting gear" table for adventures not starting at level one, a character (or party, depending on loot-sharing) should be able to obtain plate mail by around level 7; A level 5 party may be able to afford this by pooling their resources.

The tables are all somewhat imprecise, but we know that at level 5, you start with about 600GP and at level 11, you start with about 5600GP. Note that ~600GP is consistent with expected loot from CR-appropriate monsters during levels 1-4.

IF we assume that the scaling is actually linear and not tiered (meaning that a smooth-ish line can be drawn from each level's expected loot, rather than a 5th level character having 500 more gp than a 4th level character) and we use the two points mentioned above (level 5 with 600 gp and level 11 with 5600 gp), then we can find a distribution. (though, if such a graph were to exist, it would probably not be linear, but I digress)

5000GP over 6 levels is ~850 gp per level.

That gives us:

level 5 with 600GP

level 6 with 1450GP (just shy of full plate)
level 7 with 2300GP

level 8 with 3150GP

level 9 with 4000GP

level 10 with 4850GP

level 11 with 5700GP (close enough)

from which we can derive.....

Around level 7 for an individual

Around level 5 for a party

The only official element that would limit acquisition of plate armor would be its exorbitant cost. Xanathar's Guide to Everything (page 135) suggests that a party should have seven rolls on the Challenge 0-4 treasure hoard table and 18 rolls on the 5-10 table as it levels up. With average treasure rolls, with a group of 4 to 5 player characters, plate armor should probably become affordable somewhere around level 7, though that will vary somewhat depending on how much money you're making outside of hoard rolls and how many people are splitting the proceeds. (This matches my personal experience, where the paladin in our party of 5 got his first set of plate just about the time we leveled up to 7.)

But I think you have it a bit backwards; even if you strike plate from the armor list completely, it doesn't really change who wants to use their Heavy proficiency, and it doesn't make heavy armor weak or undesirable. Medium armor is only particularly desirable if you have a moderately good Dexterity; if you don't, you go Heavy if you can.

In general, you want to wear the heaviest armor you have proficiency for, unless you have a very specific reason not to -- which usually means having unusual stats for your class (such as a finesse Fighter) or having unusual needs not normally associated with your class (such as stealth).

Anyone can find an armor to get to AC 16 pretty easily no matter what their stats look like, unless they've managed to submarine both their Strength and Dexterity.

AC 17, the maximum for all non-Plate armors, is pretty easily achievable if you care to go there, but it's a lot cheaper and easier for Heavy armor wearers, provided they can handle the weight (which generally means a good strength score or being a dwarf).

In other words, if you hit AC 17, you're doing well and have effectively maxed out your defense from armor. Plate is a little extra thing to stand above as the Ultimate Armor, and with a price-tag to match. But if you exclude it from your game or make it prohibitively rare, the fighter and paladin (and some clerics) are STILL going to probably wear Heavy armor, just because it's the easiest path to AC 17 and matches their usual stats well.

It might be different if stat bonuses were easy to get, but since they aren't, you usually need to focus stat increases on your core abilities, which doesn't often leave lots of space to buff your Dexterity out of the Heavy armor range; and having heavy armor available is what allows these characters to distribute their ability points elsewhere.

As early as they can afford it

1500gp is a lot of money in the beginning, later it becomes trivial.

The trade of magic items is limited in 5e, so it is very hard to spend money meaningfully, especially if you artificially restrict other pricey goods.

Balance

Dex primary classes tend to max out their AC at level 8*, so the Heavy Armor wearers should not be later either.

*) Fighters at level 6, assuming point buy