I guess most of us are here because we're fairly IT literate and or inquisitive enough to learn. What you're describing makes sense on a technology level to us but it's missing the key ingredient that going to make it work for the government.... the human ability for incompetence, exacerbated by British hubris, made worse by multinational IT consultancies having a stranglehold on UK government department IT. Ok that's more than one missing ingredient 🤣.
The easiest thing to do would be to mandate MPs use separate phones. One for personal use one for government business. Great. What happens when they don't? You're going to have a large number of MPs that will simply say, "I am elected you are not I will only carry a single phone". What do you do then? Mandate a work profile? Again, "I am a duly elected member of this parliament and I am not going to comply". They'll just swap personal numbers like they do now and continue to use private WhatsApp for government business. It will go on and on like that because they'll just be belligerent for the sake of it. It's the British way. Under those circumstances I simply can't see educating MPs or civil servants on how to use a (let's be honest) niche messaging app. People are inherently lazy and they'll choose the path of least resistance even if that means weakening security and obfuscating government records. MPs don't give a shit. Can you see MPs voting on strict controls for themselves? I can't.
Let's assume for a second that this does have by in from government. Every department has their own long running deals with US IT consultancies that aren't simply going to allow these types of changes that undercut their bottom line. Who do think runs all the various IT systems in the UK government? Its not the Department For Information Computing & Technology (DICT) its several large consultancies (Microsoft, Amazon, IBM, JPMorgan, KPMG, Deloitte, etc etc). They're not going to hold out their arms and welcome an in-house solution that under cuts their bottom line. Just ask GDS!
I'd love for what you're suggesting to become a reality but we have enough difficulties getting public data from local councils in usable formats let alone trying to swing government departments to do anything useful.