CAPTCHAs are annoying and I don't need a better reason than that to want them gone.
But, taking the argument of ACCAN, their alternative doesn't hold up. They are limiting themselves to registration forms for signing up to websites which is a valid issue but not the only instance where CAPTCHAs are used.
Thankfully not all websites require you to sign up to use them (yet) and so there are a lot of CAPTCHAs in use where the proposed solution of sending an e-mail just doesn't make any sense.
To find a real alternative, you have to start by asking what the product does.
The purpose of those annoying scribbles is to verify that a human rather than a 'bot' is interacting with the website. Further, it is doing that in the website, without the any additional processing from the user OR the site operator. FURTHER, it is a bit of bolt-on code that requires no additional infrastructure, maintenance or support from the website operator.
Compare that feature-set to 'just send an e-mail'. That 'solution' addresses none of the above points.
There needs to be a better solution but I think it's naive to just blurt out a 'common sense' answer, without accepting that if a workable alternative was that simple then we would have it already. There is a reason why 'just send an e-mail' isn't on the W3C's list and it's not because they haven't thought of it.
There's also a reason why none of the proposed alternatives have gained any acceptance, and that is because they are intensive to implement. A small business can very easily add a CAPTCHA to their website. Try adding 'Heuristic checks' to your small business's website!
I agree with ACCAN - they are difficult for even the most sharp-sighted of people to use so it is evident they would pose problems for others, less able users (including the elderly). I just think they need to recognise that the solution isn't that simple.