I believe it's a good move
You're right but generally the ASA are a very easy group to work with as a consumer. Firstly they always respond and they always act and they always tell you what they did. I've used them to take down numerous pieces of misleading advertising for snake-oil. Now I will be able to do the same not just for adverts in emails but claims on their websites.
Previously I had to go through the OFT for the latter which is fine but the OFT have no requirement to tell you what actions they take so you're not always sure if they did anything.
The ASA will refer complaints to the OFT and the ASA has a simple webpage for you to register your complaint, unlike the OFT. Makes the process that much easier for the consumer.
It also means another avenue of 'attack' for campaigns. For example the Chiropractic complaints that recently led to some 25% of all practitioners in the country being placed under investigation for misleading claims could now also be referred to the ASA. A three pronged attack via the ASA, OFT and Regulatory body generates three times the paperwork for the snake-oil vendor to deal with. The BCA apparently had to take on new staff just to deal with the volume of complaints they received and it could have been so much more work!
And while the ASA might not have any teeth of their own it's at least better to have a regulator that is respected than no regulator at all.