Likely, and the fact that there are indeed varying opinions among the "elites" that aren't always spreading propaganda and information coming directly from Kreml or Putin. (Prygoszhin, Kadirov, various big milbloggers, etc)
To elaborate, this could cause a minor headache for Putin right now, but a migraine later.
Centralized information flow is key during long wars where the situation might change several times, defeats, big faults in the military and so on can be covered up, downplayed, or acknowledged and dealt with depending on the intentions of the entity controlling the information.
For example, if the letters coming from Stalingrad's German soldiers weren't censored, it could very well have been snowballed into a threat to the Nazi government itself, or at least a big dip in morale that caused even further defeats. Earlier, it seemed that Putin, or at least Putin-aligned people in his inner circle nudged the major propaganda channels in specific directions when it comes to the war, and even military bloggers that in many ways parroted what they said.
As long as there weren't any real differing opinions on how the course of the war should go among Putin's allies or personal conflicts among them, roughly the same information and the same "attitude" if you will. The information can also come from independent domestic sources and even propaganda channels that Kreml mostly nudge in different directions but are functionally autonomous.
However, considering the fact that an encrypted social media form that can't easily be censored (Telegram is very popular in the country together with various groups now vuying for the state's favour (Prygoszhin and other PMCs, Kadyrov), this informational domestic advantage the Kreml has had is weakening. Its still very big, but weakening. It would be hard for authorities justify silencing "trusted" individuals with large followings if they suddenly start to spread information that is potentially destructive to the war effort or criticism toward various leaders. Over the past months, Russia's MoD has been giving different information than Wagner about certain events, and with various big milbloggers in the mix....
There's big potential for a spread of information that will inevitably hurt the Russian will to continue to fight in very many cases because of this big mess of informational actors in various future situations. It may be because of power struggles between groups, individuals, or factions, or a major defeat that *could* potentially still be Lessened by Kreml, but if they fail to do so the blame will go in wildly different directions, and the narrative might slide out of their hands.
Now, I'd argue that democracies don't nessecarily have the same problem because of the fact that differing opinions are something to be expected, and the power struggles that do appear are not in the same level as amazingly corrupt countries.
TLDR: I think the Kreml is very concerned (especially since spokesperson acknowledged it) that interpersonal rivalries and other factors can start to disrupt the informational flow to such a grade that they themselves can't control it anymore.