The main problem for the Tarka Line, as others have mentioned, is infrastructure. There's several problems here;
- The passing places at Eggesford and Crediton only allow for an hourly service, and so even if the rolling stock was there for a half-hourly service, the line can't take them. It does mean that, apart from the occasional gap of up to 90 minutes, and Sunday services, the line is running at 100% capacity. You cannot physically put any more trains on it, so in that respect FGW have done the very, very best they can.
- Two open level crossings, at Umberleigh and Salmonpool (near Crediton) cause trains to slow to a crawl. Not such a problem at Umberleigh where almost all trains are stopping anyway, plus the line speed is only 35mph. But at Salmonpool, the line speed is 70mph, so the time penalty for having to slow down to 20mph for the level crossing is severe.
- Condition of the track. Particularly north of Copplestone, where the line speed drops from 70mph down to 55mph for almost the rest of the journey. The old jointed track was particularly noticable on the 142's, and although thankfully even the 143s make for a smoother ride, it doesn't up the speed they can do. Thankfull, 10 miles of the old track are being replaced this winter, and I believe (though I haven't seen any official sources yet) that this may mean an increase from 55mph between Eggesford and Portsmouth Arms. One area that does need doing is between Chapelton and Barnstaple where the line speed is currently 60mph, despite being dead straight, dead level and there's no intermediate stations. This section should be one where DMU's can max out (even if you need to slow them down a little earlier approaching the end of the line at Barnstaple).
- Token exchange. One-off users of the line may have noticed trains stopping, seemingly at random, on the level crossing at Crediton, and the driver get off the train at Eggesford. This is for the token exchange that allows trains to use the next section of track. Not exacly the most efficient method of signalling in the world.
Whilst sorting out all these problems would cost a good chunk of money, in comparison to the likes of the proposed electrification or HS2, it would be a tiny drop in the ocean. Would passenger number rise and the line benefit from such investment? Well, if the installation of the passing loop on the Falmouth branch is anything to go by, then they most definately would.
EDIT - I've just seen that the Tarka Rail Association's website has finally been updated, and up to the start of August passenger numbers look to be up 30,000 (from 260,000 to 290,000) - an 11.5% increase.