The reason it was changed to height rather than weight is for two reasons - the first one is that children vary much more in weight than they do in height by age (apparently) and realistically the graduation through car seat stages should happen by age, height/weight has only ever been a proxy for this and in order that the car seats are designed to contain a child of that specified size for crash testing purposes.
The second reason is that in most of Europe, children's clothing is sold in height bands rather than age so most parents have a rough idea of how tall their child is all the time even without measuring them. You know if they are wearing size 98 clothes, they will fit fine into a seat up to 105cm. So it's thought to be easier to understand. It also is easier for car seat shops to provide a height chart than a set of scales.
You're right that practically, the important part in terms of safety of fit is the size of their body from bum to shoulder. And TBH for most seats on the market for this reason it's not likely to matter that much if they are e.g. 107cm in a 105cm limit seat. There are exceptions, but generally the height limit is a bit less strict than a weight limit was.
The height limits of 75cm / 87cm / 105cm / 125cm are based on the old weight categories which were 10kg / 13kg / 18kg / 25kg and roughly correspond to 9 months / 18 months / 4 years / 7 years. Obviously if your child is taller or heavier than average, they might not fit into these categories.
However if you're talking about a baby, I don't think you need to worry overly about a 125cm height limit - are you mixing this up with 105cm? 125cm on the 91st centile is 6.5 years, which is unlikely to be a problem.
105cm on the 91st centile is about 3.5, which is not great but a lot of people have another baby by that age so they swap the first child into a 125cm seat and use the 105cm seat for the younger sibling.