How is this an issue? Germany implemented UHC circa 1941 when the population was ~70M. Their population has grown since then (now ~84M) - but what's the issue? It was "cheaper" to implement then - ok - but the cost to keep it has grown since then too.
NB: China moved to UHC in about 10 yrs. 2003: Only ~20% of the pop covered 2013: ~95% of the pop covered .. and the population hadn't grown much over those 10yrs: 2003: ~1.3B 2013: ~1.35B Granted it wasn't very comprehensive coverage at the start - but it's improved a lot over the last 10yrs.