The journey lengths can be horrendously long.
I did a couple of test bookings for New York in June. The first was to JFK which would take me via Barcelona and the Azores with the last two sectors on Azores Airlines. The fare wasn't too bad but the journey time was 30 hours!
The second was to Newark which took me via Paris Orly with ORY-EWR on La Compagnie. The fare looked a bit steepish, over £2,000 one-way, until I remembered that La Compagnie is an all-business class airline. This journey too was around 30 hours.
I checked a short-haul route, Malta, which would have been via a connection at Milan MXP. The one-way fare wasn't so bad but the flight length was 23 hours. I remember checking Malta a couple of months ago in the booking engine to find there were several days a week shown. I thought I had missed an announcement only to find all the flights were with easyJet's Worldwide connections.
There are short-haul routes not available direct from BRS that have shorter overall flight lengths but they can still be two or three times the length of a non-stop flight.
I tried a test booking for Tel Aviv and picked 21 February at random and found there were seven flight options that day from BRS involving changes at Geneva, Amsterdam, Berlin or Paris CDG depending on departure selected from BRS. All involved overnight stays en route with overall flight lengths ranging between 16 hours and 26 hours. The fares were quite reasonable though, but you'd have to balance that with overnight accommodation costs at the en-route airport. There might be other days when it's possible to get to Tel Aviv without an overnight stop.
About 20 years ago before BRS had direct scheduled flights to Geneva I persuaded my wife to use KLM from BRS to reach Geneva for a holiday instead of driving to LHR. We had between two and three hours on the ground at AMS between flights in both directions which wasn't too bad at all given the alternative was a drive to Heathrow and a drive back afterwards.