I’d guess a sizeable majority of convicted murderers never set out with a premeditation to kill.
I'm no expert but the data I've come across, certainly for the UK and US, is a bit of a mishmash that suggests quite a lot of complexity.
For example, I think in the US there's been studies on domestic violence related murders that showed there were two distinct categories of murder. The first were homicide-suicides (where the murderer kills themselves immediately after) and typically these differed from straight homicides in that the homicide-suicides were generally premeditated and planned and the straight homicides were not. So at a practical level it appears the majority of DV murderers who are around to stand trial/be sentenced have typically not set out with a premeditation to kill.
However when you look at the circumstances of these 'non premeditated' murders, often patterns emerge of behaviours and thoughts in the run up to the killings around controlling behaviours and thoughts of violence, alongside in some cases actual acts of violence that don't go as far as murder. So whilst the ultimate act itself might not be explicitly premeditated it is also not really a spontaneous 'crime of passion' as traditionally they were framed.
Studies also show that premeditated killers more often have a quite specific mental disorder/psychopathy whereas more impulsive killers typically have lower than average cognitive abilities and often some form of drug is involved when they kill.
Though domestic violence is only one context, studies show similar kinds of complexity and issues in other contexts.
So whilst I think your assumption that the majority of murders are not premeditated, in that they are not planned out in a detailed fashion, is probably true (and UK Home Office data would support that view too); at another level many of those non premeditated murders are actually to some degree quite predictable and are not the result of a single unknowable aberration. If that makes sense?
At a practical level if we are talking about reducing homicides, nothing suggests that things like capital punishment would make any difference. Earlier identification of and intervention around abnormal behaviours would be much more valuable.