Honestly, I do wonder whether people posting on this thread actually live with people working in sport – not playing it, that is completely different, but being immersed in it as a professional career.
@Thepleasureofyourcompany you are correct, there are thousands and thousands of jobs in sport, ranging from the already-mentioned physio, sports massage and S&C, to player performance analysis and psychology, to sports nutrition, to coaching and teaching. But on top of that there are governing bodies and organisations you can work for such as the FA, the ECB, the RFU, the BOA, Sport England etc, as well as individual clubs/teams.
Then there's event management, or marketing, PR and comms work (yes OK these might be open to other graduates too, but a sports specialist PR/marketing company is just as likely to hire a sports science graduate and teach them marketing as they are to hire a marketing graduate who needs to acquire in-depth knowledge of one or more sports).
Then there's agency-side work – there are dozens of companies who represent professional athletes, arrange sponsorship deals and media access and organise photo shoots and interviews on an individual level, but also work for brands who are involved in sports sponsorship such as Coke, Mastercard, car marques and so on. Sports science is at least as good a route into these kinds of careers as any other, and better than most.
Sports careers don't typically pay all that well, it's true, but not everyone is motivated primarily by money – particularly our DCs' generation ime – and you can certainly earn a decent living while working in a field you love.