You might be further interested to know that in addition to service ceiling, there is also 'combat ceiling', which is invariably defined as the altitude limit where an aircraft is still able to make a 500 feet per minute climb. And since you turn an aircraft with excess lift from the wings, the advantage of that in combat is obvious, hence the definition.
Naturally, that kind of ability would be useful for a fighter aircraft against a two seater, where a fighter would need the kind of maneuverability that a 500 fpm climb rate would allow, to enable it to shift about under the two seater in order to stay out of the rear gunner's sights. Therefore, it would certainly be useful for stuff like the RE8 and BE2 (and equivalent German craft) to take a fight higher than a regime where a fighter could dance about the skies, since they needed all the help they could get, and if they could get up to the kind of height where an enemy fighter was above its combat ceiling and thus limited on maneuverability, which admittedly would probably be a long winded process, then that would even things up a bit for the spotter aircraft, as they tended to be designed with stability rather than maneuverability in mind.
I don't know if that was regularly tried, but theoretically at least it makes sense, and there is some evidence that it would work if you read either Jimmy McCudden's or
Eddie Rickenbacker's autobiographies, in which both of them relate stories where a two seater is too high up for them to be effectively engaged without getting fired back at. When you think about that, there were obviously some limitations to the famous technique of tilting the Lewis gun upwards on a Nieuport or SE5 in order to fire at a two seater from underneath.
That method of attack sounds like a simple thing to do, but I'm willing to bet that it took a fair bit of skill and indeed courage to manage in reality; when your aircraft is teetering on the brink of a stall and pitched up quite nose high to maintain enough lift, the last thing you'd feel like doing was taking your hands off the stick to man a Lewis gun, possibly having to stand up in the cockpit too, in order to reload the thing, when very near to stalling and spinning, although in fairness, the SE5a did have a very good elevator trimming system which would doubtless have helped a bit. Even so, I think I'd have been very scared to stand up in the cockpit of such a craft with no parachute and a 20,000 foot drop over the side with no safety strap holding me in. The thought of that alone is enough to make you realise what a bunch of gutsy b*st*rds those guys were.
Al