Eurostar did go through Bat & Ball from time to time, as indeed did the old boat trains. This seemingly oddball (excuse the pun) route was used to relieve pressure on the two-track section between Orpington and Sevenoaks, with three intermediate suburban stations and the long tunnel at Knockholt, which together really restricted capacity for fast trains. Suburban trains terminated at Sevenoaks. Sending fast trains round through Swanley and Otford had long been practiced to relieve this, and from there it's actually quicker to go through Bat & Ball and get back on the main line again than to weave round all the curves on the Maidstone line. You can almost see between the two routes at Dunton Green, they are very close.
I recall being on a mid-morning Eurostar in early 2003 which actually did both the Catford Loop and ran via Maidstone East, as well as multiple signal stops around Swanley, grinding round through Maidstone at 30 mph and ending up at Gare du Nord about an hour late, although just in time for a very pleasant late Parisienne lunch. I wonder what the French thought of such nonsenses, and indeed what the French crews from Paris thought when route learning "by ze way of ze Bat and ze Boll".