So, signal coupling capacitors?
Distortion and microphony are the main downsides. Distortion might not matter, depending on how they're being used (active clamp DC-restore per line/frame?), but microphony has the interesting effect that you'll see horizontal luma bars when tapping on the circuit (or there's enough ambient audio).
The ideal choice here is tantalum, actually. At least, electrically speaking -- but their cost (in general, plus externalities, i.e. Ta is a conflict mineral) may be sufficient reason to stick with electrolytic.
Or film, but large values in low voltages are prohibitively large; film just can't be stretched as thin as ceramic can, without succumbing to thinning or pinholing.
On the upside, they see very little if any ripple current, or heat, so shouldn't need replacing unless they were poorly made in the first place. (Seals can go leaky, electrolyte can corrode, etc..) This is one place where an ESR test (in circuit should even be reasonable) is preferable over a general "replace everything" policy. Anyway, modern electrolytics will be good for at least another couple decades at room temperature, so it's not like you're dooming the unit by replacing like with like.
Tim