SWT has been trialling smartcards for gold card holders but is having a number of technical problems. I would rather see a national scheme paid for by central government, letting each TOC do their own thing will just lead to lots of marginally different systems which will probably not be interchangeable among operators and which will be largely paid for from Dft money anyway.
SWT's scheme includes 7 day seasons now, at least it definitely does between Basingstoke and Weymouth. Also, AFAICT they aren't 'doing their own thing' but just attempting to make the DfT's pet ITSO system work, just like LM are trying to in the Birmingham area.
None of the TOCs that are currently required to introduce 'smart ticketing' have any option other than ITSO, according to their respective franchise specs.
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An oyster scheme would just be too complicated to implement I suspect. Somewhere like where upon purchase of a ticket it is loaded into a card would work though.
You have to differentiate between the two separate modes of TfL's Oyster system. Oyster started out with Travelcard seasons only. Seasons on a National Rail smartcard would be just as easy, no problems there other than kitting out staff to be able to read/check them.
A few years later Oyster added pay as you go, (PAYG) functionality. It is this idea of stored credit that would be incredibly difficult on NR, as you suggest, unless it was confined to discrete local areas.
AIUI a national smartcard on the ITSO principles could contain, say, a Tyne Wear Metro PAYG stored credit for use in that area, as well as a separate stored credit for TfL Oyster, maybe even a hypothetical South Hants scheme. Whether or not they could share the same cash I don't know - probably not, as basically the stored credit value goes straight to the Metro or TfL or whatever when you load it, although it can be refunded if not used.
What you'll never see, as far as I can work out is a means of touching in at Southampton Central, and out at Tynemouth, having travelled via London, with a correct fare for the time of day being calculated 'on the fly'. For that journey you'd have to pay up front - and there'd need to be some processing done to make that prepaid ticket overide any local schemes that you happen to pass through en route. Hope that makes sense...