There is more work for you to adjudicate which effects will cause damage. It would make destroying objects a lot easier. Additionally some effects with saving throws don't make sense for objects. Finally it may be unfun for your players.
Extra work for you
The game has been balanced around the assumption that objects are hard to destroy unless they are explictly targeted. It makes the game simpler.
The effects that damage objects are intentionally few and far between. For example Shatter specifically damages objects, while the spell Blight does not (unless the object is a plant). Because of this you will need to consider which damage types will damage objects and which won't.
- Does it make sense for psychic, poison or necrotic damage to affect objects?
- Are there damage types that objects might be specifically vulnerable to?
- Do those vulnerabilities depend on the material the object is made of?
You will need to track which objects are in range of the spell, what they are made of, and what vulnerabilities and resistances each object has. Taking all of this together means you need to be more meticulous when you map out individual environments, with exact placements of objects.
Easier to destroy objects
If all AoE spells damage objects, then they will also damage buildings. Damaging buildings is something spellcasters in particular will want to avoid (espescially if they are in them). As a result you would expect magic users to want to limit the damage they do to structures.
Any self respecting adventurer wants to maximise loot gained and minimise the effort to get that loot. AoE spells satisfy both of those criteria, but only if they don't damage the loot. By making these types of spells damage objects you are changing the motivations of the generations of spellcaster who went before your players.
Unfun for your players
Changing their AoE spells to cause damage to objects will mean your players end up damaging their loot. The two potential effects of this are:
- it will cause your players to have less loot
- or will make their AoE spells significantly less useful
Neither of these outcomes will necessarily be fun for your players (or at least for most players). Battles with lots of enemies will be harder and/or the players will get rewarded less for having those battles.
Does all of this mean you shouldn't do it?
Not necessarily, but I would recommend talking to your players and seeing if they will enjoy the change.
Ultimately when we play D&D we are playing a game, not a reality simulator. The aim of games is to make sure everyone playing has fun (including the DM). If a homebrew rule change is implemented that potentially could make the game less fun for the players, that change needs to be discussed.
The flip side of this question is, of course, does the suspension of disbelief caused by not having this change make it less fun for you as the DM?
Only you can answer this question, but it should form part of the discussion you have with your players.
Does the game have rules for improvising this sort of damage?
Yes. Chapter 8 of the gives a table which sets out different levels of improvised damage, with suggested examples. Using this table, along with the damage output by the spell or AoE effect, is the place to start.
A monster or effect typically specifies the amount of damage it deals. In some cases, though, you need to determine damage on the fly. The Improvising Damage table gives you suggestions for when you do so.