I had the exact same thought process about 2 years ago.
One plumber told me the problem was the old boiler being inefficient which is complete rubbish. Another agreed with me that as long as it was safe it was fine.
The payback time meant it would have been cheaper to pay higher bills.
What made my decision to have it replaced was a lack of some spare parts.
A plumber who spoke sense said it was worth thinking about changing in the next few years as a failure of some parts that he was seeing would mean a new boiler.
When I swapped I also like the idea of a hot water tank etc but decided for a Vaillant Combi - It means we have endless hot water a much simpler heating / hw system and much better hw pressure.
So far we had a pump replaced under warranty and last week the pcb changed as it was playing up. Slightly annoying given Vaillant are supposed to be v reliable but overall happy I changed from a standard system boiler/hot water tank to just a combi.