As a user, this is my take on it.
I live in a house with conventional open vented hot water cylinder, and always have done. I would need a very, very, very good reason to consider living in a house with a combi. As in, for most situations, a combi would be last (or very nearly) on my list of options to consider.
However, we've always had proper controls on the heating (something Dad was always ahead of the game on) - where we used to live, the guy servicing the oil boiler would comment on how clean it was since the stats did away with most of the short cycling that was normal for systems of that age installed with no stats anywhere.
As a minimum, consider a controls upgrade - it probably wouldn't cost much at all to get a good chunk of the possible benefits. At present (assuming there's no cylinder stat), when the system is set for hot water, the boiler will turn on and off on its own stat - regardless of whether the cylinder needs any more heat. Just adding a thermostat to the cylinder will allow the boiler to come on when the tank needs heating, and turn off again when it's hot. This would then allow you to leave the hot water on all day (or at least from before you get up to when you go to bed) with very little cost to worry about - without a cylinder stat, doing this would mean the boiler short-cycling all day.
If the system is that old, then the cylinder is probably quite slow at heating up. Just replacing it like-like with a modern fast recovery cylinder would make a big difference - after running it down, it would reheat a lot faster. The cylinder itself isn't expensive, but you'd need some plumbing changes which may be easy or difficult depending on your current system layout. If there's room, you could fit a larger one for negligible incremental cost.
Just remember that in the 60s, most systems were like you have. It was normal to put the hot water on when needed - and this was seen as a distinct advance on having to light a fire to get hot water from the back boiler ! Most also had a switch in the kitchen (or somewhere easily accessible) for turning the immersion heater on when hot water was required. These things seem quaint these days - but they were "modern" at the time.