They remain a popular system to install, new, and many installers will try to persuade you to have one as a replacement, for a stored water system. Both do have their pros and cons....
A stored water system, cost more to install, stores lots of ready to use hot water, the boiler is cheaper, and as it doesn't run every time there is a demand for hot water, as well as possibly needing a much smaller Kw, they can be more gas, plus water efficient. The boiler is much simpler, therefore more reliable, and cheaper to repair. Many of the potential faults, can be dealt with by the owner, or a plumber. Less pressure in the CH system, so less chance of leaks.
A combi boiler is more expensive to buy, a one box solution, will cost to convert an open vented, to combi. Hot water filling a bath can be much slower than an open vented, and the boiler suffers extra wear and tear, every time there is a demand for hot water. The boiler Kw will likely be much greater than needed for an open vented, so will likely need a new, larger gas pipe run to be installed. Combi's are great for small homes, flats, and can save on gas, where use of the home is irregular. They also save on space, as no cylinder, or header tanks needed in the loft.
'Should I be asking also for a quote to just replace the HWT, system clean, and boiler service.' You will need to explain, that you have an open vented system in, and you are considering either option at the moment - installing a heat-only, or converting to a combi.