It's exceptionally difficult to avoid the data being de-anonymised.

If an 'anonymised' medical record says the person was born 6th September 1969, received treatment for a broken arm on 1 April 2004, and received a course of treatment in 2009 after catching the clap on holiday in Thailand - that's enough bits of information to uniquely identify me.

And medical researchers are usually very big on 'fully informed consent' so they can't gloss over that reality, hide it in fine print or obsfucate it with flowerly language. They usually have to make sure the participants really understand what they're agreeing to.

It might still work out fine, of course - 95% of people's medical histories don't contain anything particularly embarrassing, so you might be able to get plenty of participants anyway.

'Anonymisation' schemes are a little like encryption, in that they just get monotonically weaker over time as people work out attacks. But the attacks tend to be much worse. I work in academic open data publishing, and the netflix prize (https://arxiv.org/abs/cs/0610105) hangs over our heads.

But what this illustrates to me is that researchers are just really careless, despite everything we make them agree to in data transfer agreements. It seems absurd to have little cubicles like this https://safepodnetwork.ac.uk/ (think Mission Impossible 1) but I do despair.

You mean giving anyone access to the data? Or open sourcing the code? If the latter, I think that's a generally a good practice. Security through obscurity is never good for public infrastructure. In this case, UK Biobank has now switched to a remote access platform (not particularly secure, as the data was found for sale on Alibaba today), but contracting it to DNAnexus and Amazon. Private companies have no incentives to open source data, unless mandated to do so.

In the EU, there is a bigger interest in building scalable but also secure platforms for health data. Hopefully good innovation will come from there.

The people who agreed to contribute their biodata did not consent to that.

If you want such a project you need to have a new project with a different agreement. I doubt you could get as many volunteers to freely give away such intimate data to anyone who wants though

One of the most important "con"'s is that without controls, fewer people will allow their data to be included in the data sets.

Hard to do. The same people with the collection and tracking infrastructure required are infinitely sue-able so you need legal protection if anything goes wrong.