For the purposes of this answer, I am assuming that the DM is running everything just as given in the book, even when they are just recommendations or suggestions and the rules explicitly acknowledge the possibility of exceptions.
The rules don’t really entitle you to anything
You are affirming the consequent, unfortunately. The rules state that if an item costs more than the town’s limit, you definitely won’t find it. The converse, that if it does not cost more, you definitely will find it, is not necessarily true.
I personally think they should...
Now, generally speaking, I think this is a problem and that the rules more-or-less should also guarantee that items within such limits are available. Many classes are utterly dependent on magic items, and not just on the general concept, but on getting certain specific magic items, to function on anything like a level-appropriate level. Failure to get them results in a character significantly less powerful than his or her level would otherwise indicate, and the exact degree to which his or her power has been reduced is rather difficult to judge. (Of course, this would matter a lot more if CR was at all reliable to begin with, which of course it is not; encounters were judgment calls anyway. But exacerbating that unreliability by moving away from the assumptions baked into the system only makes such judgment calls harder.)
...but would make partially-charged wands an exception to that anyway
But in the case of partially-charged wands, those are particularly problematic. A 1-charge wand costs 60% what a scroll of the same spell at the same caster level costs, but is more durable, more easily kept accessible, and easier to use (both for spellcasters and those making Use Magic Device checks). There is therefore absolutely no reason to ever have a scroll if you could get a 1-charge wand instead.
Furthermore, you cannot make partially-charged wands: new wands always have 50 charges. They only become partially-charged through using up charges. Therefore, no one can make a business crafting and selling partially-charged wands: the only place you could hope to find them is in a pawn shop. This gives a rather significant reason why you should not expect them to be regularly available.
There's no perfect way to assign rarities to all the tables.
I made a spreadsheet counting the percentage of items of each rarity1 contained in each of tables A through I. These results are as follows.
\$
\begin{array} {c|r|r|r|r|r}
\textbf{Table} & \text{Common} & \text{Uncommon} & \text{Rare} & \text{Very Rare} & \text{Legendary} \\ \hline
\textbf{A} & 50\% & 50\% & & & \\ \hline
\textbf{B} & & 100\% & & & \\ \hline
\textbf{C} & & 14.3\% & 85.7\% & & \\ \hline
\textbf{D} & & & 6.3\% & 93.8\% & \\ \hline
\textbf{E} & & & & 42.9\% & 57.1\% \\ \hline
\textbf{F} & & 100\% & & & \\ \hline
\textbf{G} & & 2.1\% & 96.8\% & 1.1\% & \\ \hline
\textbf{H} & & 2.9\% & 8.7\% & 88.4\% & \\ \hline
\textbf{I} & & & 7.8\% & 23.4\% & 68.8\% \\
\end{array}
\$
As can be seen, only tables B and F are completely consistent in their rarity, so it's not possible to assign a rarity to every lettered table perfectly.
But there's a better way to solve the problem.
The problem isn't really what rarity to assign each lettered table. It's how to preserve which rarities become available to a character when they reach a specific tier and at a particular point cost (according to the Shared Campaign rules being used). For example, it doesn't matter that table I contains a mix of very rares and legendaries. What matters is that major legendaries only become available at tier 3 for 12 points, and only table I has them, so for all practical purposes when a character becomes eligible for table I then they become eligible for major legendaries.
So, how to solve that version of the problem...
Observe when each minor and major rarity becomes available to a character for the first time based on tier requirements, grouping any rarities that share a tier requirement and point cost.
Observe which lettered tables cover each minor and major rarity most precisely, grouping any tables that share a tier requirement and point cost.
See if we can find an obvious mapping from the table groups in step 2 to the rarity groups in step 1. If so, we can refactor the purchase options.
My observations for the minor items are as follows.
- Commons, uncommons, and rares start at tier 1 for 4 points. Tables A, B, and C (plus the minor commons in Xanathar's) almost perfectly2 cover these rarities.
- Very rares start at tier 2 for 8 points. Table D almost perfectly2 covers this rarity.
- Legendaries start at tier 3 for 8 points. This rarity is exclusive to table E.
My observations for the major items are as follows.
- There are no commons.
- Uncommons start at tier 1 for 8 points. Table F almost perfectly2 covers this rarity.
- Rares start at tier 2 for 10 points. Table G almost perfectly2 covers this rarity.
- Very rares start at 3 for 10 points. Table H almost perfectly2 covers this rarity.
- Legendaries start at tier 3 for 12 points. This rarity is exclusive to table I.
I think an obvious mapping has emerged: in the table of magic item purchase options in Xanathar's (p. 174), replace each of the lettered tables with the following minor/major rarities and then ignore tables A to I in favor of the minor/major rarity tables in Xanathar's.
- A, B, and C (as a group): minor common, minor uncommon, and minor rare.
- D: minor very rare.
- E: minor legendary.
- F: major uncommon.
- G: major rare.
- H: major very rare.
- I: major legendary.
Although this mapping is not exactly equivalent to the way the purchase options were originally presented, the scenarios where a player could buy an item earlier or later than the original options allowed are essentially edge cases that balance each other out.
This mapping ought to allow the players to use the tables in Xanathar's instead of the DMG's tables A through I easily without deviating greatly from the balance apparently intended in the original options, which was the real problem to begin with.
Footnotes on My Methods
These percentages are according to the rarity of the item names listed in the table, not the probability of randomly generating an item of each rarity using the table's d100 column, since we're not trying to generate random treasure. Data entry errors should be insignificant.
When I say "almost perfectly" I mean there are on the order of 5 outliers out of just under 400 entries, which is insignificant. Note that by "entries" I mean the number of item names listed in the tables preserving duplicates across tables, not the number of unique items described in the book, which is far fewer.
Best Answer
On page 133 of the Dungeon Master's Guide, there is a table labelled Magic Item Rarity which gives a rough guidelines on the value of magical items, from Common rarity (for 50gp upwards) through to Legendary rarity (for 50,000gp or more).