Sometimes, if amount is small, the 0.1~0.5% difference may not worthwhile to purpose transfer the money around, time, parking, petrol may be more than the extra interest earned. Eg. 10k FD with 0.2% difference, is Rm20 pa. Purposely go to bank, withdraw and drive to ten of km away, then parking fee, the total amount of fuel, parking fee, toll fee may also reach Rm20.
Unless one doing in convenience, and having time, then it is another story.
Convenience, prompt good service also a consideration, not solely rate.
I had bad experience with one bank, that I had met no less than 3~5 time offline issue, which I unable to do any transaction when their system was offline, waste plenty of time and effort, so even they may offer a better rate, I also give it a skip.
Agreed on the add'l points you mentioned including convenience, service, time other than the rates. CB wise has phone banking service which is good so I did not think of the other points you mentioned. But for other banks, we have to consider the other factors other than rate increase.