A Staff of the Magi has the Spell Absorption trait (emphasis mine):

While holding the staff, you have advantage on saving throws against spells. In addition, you can use your reaction when another creature casts a spell that targets only you. If you do, the staff absorbs the magic of the spell, canceling its effect and gaining a number of charges equal to the absorbed spell's level. However, if doing so brings the staff's total number of charges above 50, the staff explodes as if you activated its retributive strike (see below).

The staff also allows you to cast several spells at-will (emphasis mine):

You can also use an action to cast one of the following spells from the staff without using any charges: arcane lock, detect magic, enlarge/reduce, light, mage hand, or protection from evil and good.

Can two creatures - each with a Staff of the Magi - take turns casting enlarge/reduce on each other, regaining two charges per round? Is there some reason why this wouldn't work?

A reasonable response to this would be "how did two characters get the same legendary magic item?"

Unfortunately, Season 8 of Adventurers League allows any Tier 3 or higher character to purchase one. Barring edge cases, any character that plays three 4-hour sessions at Tier 3 or 4 (enough to level up one-and-a-half times) can grab a shiny new Staff of the Magi off the shelf.

This question is related to "Can an ally charge your Staff of the Magi before a long rest by casting a bunch of spells at you?" The difference is the source of spells. Some magic items, like a Ring of Spell Storing, interact differently with spells cast from spell slots vs magic items. I want to make sure I'm not missing any pertinent details.

This seems to work

Casting a spell from an item still counts as casting a spell. See this answer for a good explanation. The simple summary is that most items contain the text:

... you can use an action to ... cast one of the following spells ...

You are casting the spell. Or in this case the other holder of the staff is casting the spell.

Enlarge/reduce targets only a single object/creature. If you target the holder of a Staff of the Magi, this is a valid trigger for the staff's ability. As your linked question says, there is no requirement for the attacker to be hostile.

Yes, two Staff of the Magi wielders can fully recharge the staffs for free in just over 2 minutes (from empty).

This may sound over-powered or totally broken, however it isn't as bad as it sounds. As @BBeast pointed out in a comment on this answer, having a fully charged Staff of the Magi isn't actually ideal. You could easily argue that the defensive benefit of absorbing incoming spells is actually more useful than the casting ability.

Therefore it is a better idea to keep the staff with only 20-30 charges. This number of charges can easily be maintained day to day by expending the unused spell slots of your allies just before the end of a long rest. The advantage this exploit grants is the ability to quickly recharge the staff after each encounter, so still very powerful, but no more-so than having two Staff of the Magi in the party in the first place.