Allowing sneak attack on improvised weapons could be unbalanced
In this situation there are four very distinct groups of improvised weapon that have different answers:
- Improvised weapons that resemble finesse weapons (glass bottles, cutlery, fire pokers, etc.)
- Improvised weapons that resemble other weapons
- Improvised weapons that don't resemble any weapons
- Items that require an improvised weapon attack (Holy Water, Vial of Acid, etc.).
An improvised weapon includes any object you can wield in one of two hands, such as broken glass, a table leg, a frying pan, a wagon wheel, or a dead goblin.
The improvised weapon rules gives us a series of example of what counts as an improvised weapon. The damage type for these improvised weapons will be the same as the real weapon they are most similar to. If they are similar enough they can actually be treated as a real weapon of that kind, as given by the following rule.
Often, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the DM's option, character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus.
Improvised weapons that resemble finesse weapons
Any improvised weapon that is sufficiently similar to a finesse or ranged weapon can be treated as one. Therefore not only is it balanced to allow sneak attack on these weapons it is officially supported by the rules. These weapons will all deal a physical damage type; piercing, slashing or (rarely) bludgeoning which is a normal limitation of sneak attack.
Improvised weapons that resemble non-finesse weapons
For improvised which resembled larger, non-finesse, weapons allowing sneak attack may be slightly unbalanced. For instance allowing sneak attack on attacks with a tree branch treated as a great-club would allow a multiclassed character to use both sneak attack and great weapon fighting on the damage roll of the attack. Re-rolling 1's and 2's on sneak attack would be extremely strong.
Improvised weapons that don't resemble any weapon
An object that bears no resemblance to a weapon deals 1d4 damage (the DM assigns a damage type appropriate to the object).
In damage terms these truly improvised weapons are the same as daggers other than the fact they lack the finesse property. By RAW you would not be able to sneak attack them, however in damage balance terms there is no issue allowing it. Even with feats to improve improvised weapons these will always be inferior to a simple dagger.
Items that require a improvised weapon attack
From the description of Holy Water we get:
Make a ranged attack against a target creature, treating the holy water as an improvised weapon.
This rule describes how to calculate the attack roll for holy water. Specifically it says to treat the attack as an improvised attack, not treat the holy water as an improvised weapon which resemble a ranged weapon you are proficient with.
Allowing sneak attack on items like this opens the possibility of sneak attack dealing non-physical damage types. As the physical damages types are commonly resisted at higher CRs this would be a bump to the power of the sneak attack feature. Allowing rogues to deal large amounts of radiant damage significantly steps on the toes of clerics and paladins (as per Someone_Evil's answer) and other items (i.e. Alchemists Fire) would allow them to step on the toes of other casters.
As David Coffron points out allowing sneak attack on items that only require an object interaction and not at Attack action is very strong. The thief's fast hands feature would allow sneak attack on a bonus action in addition to on a readied action. Multiple sneak attacks per round is a huge boost to damage output and allowing it so easily would be unbalanced.
Thematically it's wrong
A side note to the balance concerns, thematically sneak attack is 'precision damage'. There is no way to be precise with a splash weapon. I don't even the DM who has to figure out how to narrate sneak attack from a character throwing a table at something.