For example, I'm being paid 0.3% on a current-acount-linked savings account. If I could switch that to NS&I (1%) more simply than I can currently, I would. But given the relatively low amount in the account, and how much I feel my time is worth, it just doesn't feel worth it to me. Yeah, I'm lazy. But so are lots of other people, and it would change the dynamics of the savings account market if it was easy enough to make me want to switch.
In the end, I believe the best course of actions would to simply make account numbers transferable. There's no good reason why I shouldn't be able to switch my bank and keep my account number etc just like I do with my mobile phone number and provider. Of course, Bank Codes being used makes this more difficult (thank you, regulation).
https://www.currentaccountswitch.co.uk/Pages/Home.aspx
https://www.currentaccountswitch.co.uk/SiteCollectionDocumen...
As you say though, there are so many complicated conditions around getting paletry interest rates - only available on first £5k, or rates that reset to 0.1% after 12 months - that I'm not sure people would change much anyway.