I'm not sure anyone has ever suggested that it will (other than effectively by chance). What it IS intended to do is put another level of difficulty in the way of terrorists - making it more difficult for them to plan and carry out whatever it is they are doing, making it more likely that they are challenged / caught when going about their business, basically putting them on the back foot a bit. (This is the same rationale as behind a lot of stop and search and other proactive police activity - it is a deterrent to some extent, it is an exercise in crime prevention rather than crime detection.)I'd be amazed if this law caught a single terrorist...
It is also intended as a reassurance exercise - the majority of people feel safe when they see high-visibility police presence / activity and they do not necessarily associate that with any empirical measure of effectiveness of that activity (see everything from "We want more bobbies on the beat" onwards!).
Whether or not these two outcomes merit the effort and the downsides you mention is a moot point ... but they should be taken into account in the debate.
The blame culture which infests this country, particularly in the media and amongst politicians, is behind a huge amount of what is perceived as (and actually is, in many cases) excessive police activity - if something does go wrong (as it inevitably will one day no matter how restrictive you are) there is a chorus of allegations that police fucked up (witness the ongoing allegations that the police should have been on top of the 7/7 bombers even though they were way, way, way down the list of probable / possible suspects in the intelligence gathering operation ...).... doubtless because they're afraid of letting a terrorist slip through. Hand-wringing is the order of the day.
We need to grow up and accept that nothing is perfect and things will always go wrong - you simply cannot legislate all risk away in all situations and we fuck up a huge amount of other things in society if we try. (This applies equally to the current fuckwittedness about swine flu; the worst excesses of the health and safety regime; the "compo" culture we seem to have developed; the ridiculous levels of vetting for anyone that may walk past a child in the street next Tuesday; the mindless application of the Data Protection Act which gets in the way of (e.g.) protecting the public from fraudsters ...)

) ensured regular contact with Joe Public. I suspect that this unofficial and practical contact did far more good that cultural change and partnership.
) ... but lets not also forget that changing organisation culture (which is sort of the core thing we're talking about here) most definitely requires leadership!
) wouldn't be needed for these, and now abuses have led to the met to restrict it's use on the streets, it seems it'll mostly to be used to search people at train stations. 