My experience is exactly opposite: allowing player declared rolls meant that there was a reward mechanism for interrupting with a roll to gain more knowledge or effect a solution to a problem more quickly. Not allowing them has meant, for me, fewer interruption when I'm setting the scene or describing a new development -- my players have learned that more information is being provided if they listen, and even more on a clearly stated approach.
Further, and this is a point, if my players have to declare an approach and goal instead of just a die roll, there's less interpretation on my part as DM. For example, let's say there's an altar to an evil god that will explode with necrotic energy if touched by a non-worshiper. There's a big point of different to a player declaring they're closely inspecting the alter, but not touching it, to see if there's anything special about it vs a "21 Investigate!" The former nets information without danger, the latter is up to me as DM if I think a "21 Investigate!" means you touched the altar or not. And, if there's a secret compartment that can be found via physical interaction but not via looking, the "21 Investigate!" player might be upset if I decide they don't touch the altar but also don't find the secret compartment, provided, of course, it's found through other actions later.
Telling me die rolls means I, as DM, have to determine the details of your approach. Having the player state and approach and goal and then the DM asking for a roll if the outcome is uncertain and fraught means there's never any 'but my character wouldn't have touched the alter when he investigated it' going on.
ETA: and @iserth said this earlier and more succinctly, and I missed it.
GM is describing alter and...
1 - player says "i want to examine the altar"
2 - Player says "i want to examine the altar and i rolled int lore 21"
3 - Player says "i examine the alter and i rolled int religion 21"
4 Player says "i want to examine the alter and i rolled wis perception 21"
Now, i know it might come as a shock to may here but, all four of those are disruptive, not just the ones where the dice hit the table.
Really, they are.
Secondly, I know it might come as a shock but, all four of them have insufficient information. As a Gm i would ask a leading question for all before giving a response. (Maybe some will say in cases where dice are not touched they players never ever provideinsufficient info on their first description, but thats not my experience.)
Thirdly, I know it might come as a surprise to some but the cases with the dice rolled actually DID provide more information - about goal and about technique because by identifying the skill and proficiency used the gM knows what that skill and ability can provide as well as the ability being used.
Fort example, if one were to proceed from there to resolution, I would make per check generally descriptive, showing things like how much its looks to have been tended how old it looks etc from where they are. if it was the lore i would work off the notion of what general knowledge would saay about this area, how long ago temples were built etc. if it were religion, i would describe the symbols, trappings and what gods or kinds of gods or spirits the pchartacter could recognize.
Again, all from where they are there.
However, my general response to that would be to, nod in there direction and continue my description and once i got to "player action" stage deal with their inquiry. Then after the session if this showed as a regular thing, i would remind them individually that its best not to interrupt any other players if its not an emergency. thats just rude behavior.