Its been looked at but the low number of flights required per year, the vastly cheaper cost of doing it via a third party (e.g. they provide the airframe and we run the mission) and the fact that bluntly for many years OS was a bit of a backwater for all of NATO means its never been seen as a high enough priority when other needs were greater.
The majority of participating nations don't actually own an aircraft, and do lease arrangements simply because the number of flights per year permitted under the treaty means its not a great use of a very tight defence budget to maintain a bespoke aircraft type.
As for the specific platform, part of the challenge is that it requires a lot of modifications, is treaty constrained by what it can and cannot carry, and so Rivet Joint is emphatically not something we'd want to see used. The cost of maintaining a fleet within a fleet is substantial (hence retirement without replacement of the Andover) and isnt' really credible.
There are some things that really worry me about HM Forces, but the lack of a dedicate OS platform isn't one of them! What matters is the political participation - e.g. ensuring a UK led team is involved in some form - the manner of how we get there and do the mission is arguably secondary to being there in the first place.