It could, but then bearing in mind how bad Google are at suggesting ads to me, despite having all of my emails, all of my searches and a script tag on 90% of the sites that I visit, I'm pretty sure that the government wouldn't be able to glean anything particularly useful that way.
Remember: Real life != Hollywood portrayal of real life.
Suppose a future regime decides to crack down on "dissidents". They type something like "trade union" into their database. The database can then return all the details of people who were on trade union mailing lists, frequently mentioned trade unions, details of all the people they emailed regularly with extra emphasis on those they emailed about trade unions etc... I recognise that's not within the scope of the current plans, but once the monitoring equipments in it's easy. And if their equipment monitors in real time they don't even need to create a database of everything - only those email that mention "trade union", of the term of interest.
I think you're misunderestimating the scale of these challenges and how much they would cost. Google has a revenue of 37 billion dollars. ALL of the UK intelligence agencies have a COMBINED budget of $3bn - and that's to pay for computers big enough to crack encryption, to train and deploy spies to dodgy countries, to pay bribes to informants, to upkeep their top-secret cleared buildings, to do the vetting of their staff and then you want them to also keep and process petabytes of information on a scale, and with a precision vastly exceeding Google. Even if they wanted to, they simply couldn't on a budget that small.
I don't think anyone's really explained how the current plans are going to be paid for yet...
It seems to me that the emails are more about having a log for when stuff goes wrong than to have a monitoring system. When that french guy went around killing children he was a sociopath, but at some point prior to then he became a sociopath. Understanding how and who influenced him is more important now that he's been killed than the emails he sent during his final days - but because there wasn't a warrant out for him, there's no way for the french to find out who radicalised him. Now if only there was a log going back two years that they could take a look at...
So we should log all my communications
in case I commit a crime because I'm a potential criminal because until I should be considered a criminal until I die without committing a (serious) crime. Essentially what you've said above is that we should no longer treat people as "innocent until proven guilty"; but "guilty until proven innocent". The presumption of innocence is the basis to the implementation of the whole of modern western justice. As soon as this principle is upended it's only a matter of time until we end up convicting innocent people (in fact, in the case of "terrorists", we already imprison the innocent people - we just skip the conviction stage). If you're innocent (and we must presume you are without evidence to the contrary) the government have no reason, nor right, to interfere in your life more than is absolutely necessary to fulfil the aims of government (what those aims are/should be is a different discussion, however).
Hitler is a good case in point - he didn't need a big database of emails to do terrible things. If your country gets to a point where they've elected a sociopath, it frankly doesn't matter whether or not they have a big bag of emails - the country is screwed regardless. And let's remember that politicians won't have access to the emails.
Germany never actually elected Hitler to run their country, per se - he was the last available option after all the other potential chancellors had failed. And while Hitler didn't have something like this it doesn't mean it wouldn't have been useful to him. And the fact that politicians won't have access to this is little comfort - the likes of Hitler rarely obey the rules (although in his case article 48 of the Weimar constitution effectively allowing the president to suspend the normal democratic processes helped). Also bare in mind that a simple majority is all that's ever required to change a UK law - something most governing parties have so a law preventing politicians having access is not going to be much of an obstacle.
Those people in those positions haven't been security vetted to top-secret clearance and told that if they look at someone's emails without a warrant they'll go to jail for 10 years and never be able to work for them again.
I fairly sure the people in those positions did know that bribery is both morally wrong and illegal and that they could face punishment if found passing the information on. I'm also fairly sure they don't let people with a known history of corruption become police officers Security clearance may stop those who've got a bad record getting a job looking at this information but it won't stop first offenders.
This database isn't about preventing crime. It's about defending our borders. They don't care if you're watching porn or downloading pirated movies. They care if you're trying to overthrow the state or kill/harm children.
If you're doing something illegal then it's already illegal and the law enforcement agencies already have the ways and means of (legally) dealing with it. If in trying to protect ourselves from these people we become like (or worse) than them what have we achieved? This is the sort of thing that separates the good guys from the bad guys and I'm afraid that even if occasionally a terrorist slips through the net a pulls of a successful attack it's the price we have to pay for freedom. In the words of Benjamin Franklin:
They who can give up essential liberty to obtain a little temporary safety, deserve neither liberty nor safety.
The I'm seeing more and more news stories here in the UK of people being arrested for increasingly trivial "offences" on twitter (for instance the famous airport "bomb threat" tweet - http://www.bbc.co.uk/news/uk-england-south-yorkshire-11736785). The BBC have even helpfully compiled a list of "things you can't say on Twitter" - http://www.bbc.co.uk/news/magazine-17530450. It really scares me tbh, and leaves me wanting to set up an anonymous twitter account via Tor and break as many of those laws as possible. (For the record, police, I haven't and I don't actually plan to.)