Attuning does not interrupt a short rest

Under the attunement rules, it says:

If the short rest is interrupted, the attunement attempt fails.

If the process of attuning to the item itself is enough to interrupt a short rest (ie, because attuning is not "light activity" as required by resting), then the item remains unattuned after the short rest as well, as stated in the quoted rule.

This means nobody can attune to anything because attuning interrupts itself: it is non-light activity you must take over a period of time that requires light activity (ie, it's a contradiction, this rule is nonsensical).

So we must conclude that attuning to an item does not interrupt the short rest, and therefore attuning to an item must fall under light activity, as otherwise the design of this mechanic prevents anybody from using it.

If the short rest is not interrupted, they gain the benefits of a short rest

If attuning to an item does not interrupt a short rest, and nothing else interrupts it as well, then a PC can gain the benefits of such a rest. This includes recharging abilities, using features that key off short rests (eg, Inspiring Leader feat, Bard's Song of Rest), and, yes, using Hit Die to heal HP.

There are no disadvantages listed while attuning to an item

Focusing on an item during attunement does not impose disadvantage to Perception checks while they are on the lookout during a long rest. There is no mention of this in the DMG. But, the DM is free to impose any disadvantages he feels necessary as part of the focus attuning requires.

Impact to the game

I feel that if my DM imposed this penalty on me, I would just ask the members of my party to attune to items over short rests only, and to never do it during long rests. And then this penalty would never come into play, which makes it, on the whole, an immaterial penalty (unless an adventure is specifically designed with this in mind).

You're correct.

Your analysis is correct--a warlock can cast some long-duration spells by effectively spending hours instead of spell slots.

This is not unbalanced (for a single-classed warlock).

First, the spell slots that the warlock recovers on a short rest can only go up to level 5. Any long-duration spell above level 5 is subject to Mystic Arcanum, which only allows the warlock to cast it once per long rest (as explained here).

So which spells on the list are both level 5 or less and last longer than an hour? My quick perusal through the list shows only Hallucinatory Terrain, Hex, and Dream. Dream is arguably a special case, and Hex only works on one target at a time because of concentration, so your example of Hallucinatory Terrain is essentially the only spell that can be "exploited" this way. Opinions may vary about whether this "exploit" is especially powerful or not, but given that it the spell is quite limited in scope and it requires uninterrupted rests, I'd hardly consider it to be abuse.

Multiclassed warlocks can benefit this way

As Bloodcinder points out, multiclass warlocks can use their warlock spell slots to cast spells from their other classes (PHB 164):

If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature...

Thus, a warlock that has levels in wizard could cast a spell like Mage Armor, take a short rest to regain that spell slot, and then enjoy the benefits of Mage Armor for another 7 hours afterward.

As for whether this is balanced, I'd have to assume that the designers considered this possibility because the rule was written out so explicitly. After all, multiclassed spellcasters are delaying (or sacrificing) their ability to cast higher level spells, so there is some tradeoff to be considered.