Earlier quoted context omitted.
While I mostly agree with your assessment you lack to point out that using less troops saves costs, bombing less cities/civilians will make installing a controllable regime to rule there easier. These are all strategic decisions. Implying Putin held back for the sake of the ukranian people is misleading.
He definitely held back for the sake of civilians. Otherwise we wouldn’t have videos of civilians stopping tanks.
That is more due to those tanks being driven by human beings than any restraint from the leadership. You can tell your tankers to ignore any civilians lying prostrate before their tracks but that does not mean they'll just follow orders - and thank ${deity} for this.