Plenty of air forces out there...
..using frontline (or nearly so) fighters for displays (as indeed the RAF did in the era when most fighter squadrons had their own team). Examples that spring to mind are the USAF Thunderbirds (F-16), the USN Blue Angels (F/A-18), Russian AF Swifts (Mig 29), and the Ukrainian AF Falcons (Su-27).
Whilst the Reds' display is undoubtedly impressive (as are the other jet trainer based aerobatic teams at a similar level, such as the Patrouille de France and the Frecce Tricolori) there is nothing quite like seeing a close formation group of jet fighters going through aerobatic manoeuvres!
Would be nice to see the Reds using the Typhoon I as a display aircraft; that delta wing would look pretty impressive in red, too.