Cache system is there for one reason: performance improvements.
So disabling any kind of cache will have an impact on performances.
In this particular scenario, disabling block html cache, all blocks that use cache will be re-regenerated every time (page load), adding extra CPU load.
When you enable the cache block html these blocks are generated only the first time and then retrieved from cache all the next times.
Note: by default only few blocks uses cache.
So disabling this cache will produce the effect that all the pages that has this kind of blocks will be slower.
It is much better to have a module that refresh invalid cache instead of disabling it