One reason for asking the question was that at the time, RIBA-run bridge competitions were proving controversial in the engineering press. This was largely because of RIBA's insistence that entrants to their competitions must include an architect on the team, a ridiculous requirement in the bridge design field (to be clear: architects can help design great bridges; they're just not essential). However, behind the scenes, there was greater discontent, with a number of prominent designers concerned that RIBA (and other) design competitions were producing designs that were structurally bonkers, and expensive to both build and maintain.
Since then, RIBA has agreed with the ICE and IStructE to allow engineers to enter such competitions without an architect (the recent architects-only ideas contest for an inhabited London Bridge notwithstanding), and to include knowledgeable bridge engineers on all bridge design competition juries. So, the question is, have things improved?
I'll cover the same six schemes as last time, to see how they've moved on, plus the one other RIBA bridge competition held since then.
River Wear Crossing

Since the end of 2008, things have gone quiet, although I understand preparatory work on the Sunderland Strategic Transport Corridor, the grandly named road scheme that the bridge forms part of, is continuing. However, as it stands, Sunderland Council's support for the Techniker design is subject to further assessment of its affordability, and central government have not yet given unconditional agreement to fund the scheme. My own view is that the present cost estimates for the iconic bridge are too low (given its profoundly unusual structural behaviour) and that it will never be built.
Is that the fault of the RIBA competition process?
I think so. The design was chosen on aesthetic merit before it was subject to a technical review by engineers with appropriate expertise, and has been allowed to gather public support before any serious attempt to review its cost or feasibility has been completed. The risks inherent in the design should have been challenged robustly before a winner was chosen.
River Avon Footbridge

I don't think the competition process is especially to blame - the winning design (by Schlaich Bergermann and Ian Ritchie) is attractive and the engineering risks should have been low. Lack of strong local commitment to the scheme seems to have been the main problem, although I have to say the increased scheme costs are a puzzle - they don't seem to be merited by such a simple bridge.
Leeds-Liverpool Canal Footbridge

The cost rise here seems largely attributable to the low initial budget of £400k, which is very low for a landmark structure, however short the span. It's not clear at all why this scheme has stopped. I think the competition organisers must take some of the blame - if funding is the issue, as seems most likely, they should be telling promoters upfront when their budgets and aspirations don't match. There's also a need to discourage competitions from being run when funding isn't secure, as the cost to unsuccessful competitors is an unfair burden - people compete in the expectation that the winning bridge will be built. Where that's not the case, prize money should be greater to reflect the greater fee risk.
New Islington Footbridge

As for RIBA's role, I think it's the same as at Bootle - the competition simply shouldn't have gone ahead if there was a high risk that entrants would go unrewarded. Competition entries here.
Sheffield Parkway Footbridge

River Douglas Footbridge

So far as I can tell, the project has yet to secure funding, and once again designers have been very poorly rewarded for a scheme which seems to be going nowhere. I've previously discussed both the shortlisted designs, and shown some of the other unsuccessful entries.
River Soar Footbridge

So, what are the scores on the doors? I make it: one bridge cancelled for definite (Stratford); three stranded without funds (Bootle, New Islington, River Douglas); one still trying to prove its feasibility (River Wear); and two don't knows / too early to tell (Sheffield, River Soar).
Looked at another way, only three out of the seven have made it as far as planning consent stage (Bootle, New Islington, Stratford). None have made it as far as putting a spade in the ground. By those measures, the RIBA design competition seems a pretty good way to get lots of publicity, but not a great way to actually get a bridge built. To be fair to RIBA, past competitions prior to these seven have not always been so unlucky - they have led to bridges being built (e.g. the Infinity Bridge, although in that case only at a cost three times what was allowed for in the competition). It's also important to understand that the process of getting any bridge built can be subject to lengthy hiatuses and false starts, so some of these bridges may yet get there in the end.
The cost to the bridge design sector of these seven competitions is substantial, and certainly well in excess of £1m. The customers don't seem to worry about that: if you could get dozens of concept designs and still pay peanuts, why wouldn't you? However, the cost to the taxpayer will also be considerable, particularly on schemes like River Wear and Stratford where substantial investment has been made in the designs.
The real question is whether there's a better way to procure a landmark bridge design. Bridges at Stirling, Brisbane and Glasgow have recently been built through the Design-and-Build route, with no evident loss of design quality, and although a risky design was chosen, the Rhyl opening footbridge may well prove to be similarly successful. Other fine bridges have resulted from the promoter going it alone and organising their own competition.
Keys to success? A clear political will, with public support. Funding in place. Inviting a small number of designers and rewarding them sufficiently to spend time optioneering rather than just being obliged to draw up their first idea in order to meet the contest's deadline. Giving engineers a strong role (design-and-build normally forces this to happen, because no sensible contractor will put forward a design they aren't confident they can build for a known sum of money).
There's no reason why all of these can't be in place for a RIBA competition, but the evidence suggests that when any one of them isn't there, the scheme will fail.
Update 15 July 2009: I'm told by Prospect Leicestershire that the next stage of design of River Soar Footbridge is about to start, progressing towards a planning application.