The problem of the ever-expanding cache is annoying but easy to deal with - Ctrl+Shift+Del, select only "cache", then "obliterate since the beginning of time".
But if you follow this procedure with your browsing history, your (or at least, my) browsing experience is significantly degraded because all your URL autocompletes are gone, at least until you re-visit all your regular sites. You can tell chrome to delete, say, just your browsing history from the last week, but that doesn't help you when what you want to do is delete all browsing history except that from the last week (to preserve your autocompletes).
It's a real PITA.
The cache is not infinite.
For that matter, I have no idea what 'infinite history' means, every browser records history and I have no clue how that could possibly impact performance in the slightest.