Flippin' 'eck! This is like being back in the office. For my sins, I'm one of the unmentionables who investigates the feasibility and if necessary, designs these things. Obviously, what I'm about to tell you only applies to the authority I work for but hopefully, it will give you an idea.
First, a few home truths about kerb side parking. There is no provision legally for people to leave their vehicles at the kerb side unless there is a marked bay which has been made by a legal order process. The reality is, that lots of people have cars and lots of people kerb park them. However, this is something that it tolerated rather than a legal right. Also, the bit of public highway outside your house is just that, public highway. Everyone has equal right to park there in that no one has any right. The purpose of public highway is for the passing and repassing of traffic. The simple solution would be, if you don't have a drive/garage, you can't have a car. However, no one would ever get voted back in with policies like that so everyone is afraid to say it. The thing is, people think they have a right to car ownership which they actually don't. I'm not trying to stir up a hornets nest here, just give a bit of background.
Where I am, we have certain criteria that much be met before we'll look at a scheme. No more than 50% of houses can have private parking. The problem must be cause by non residential traffic and there must be adequate kerb space to resolve the issue. For example, I once had a request from a 400 dwelling tower block with a road side space of about 25 metres (4 or 5 cars) permits or not, there was never going to be enough space and the problem was residents anyway.
The reason lots of schemes run during the working week/day is two fold. One, it stops commuter parking, which is he biggest issue and two, it's about enforcement. Authorities who run such schemes normally do so under decriminalised enforcement, ie, civil enforcement officers, no police/traffic wardens doing it. Therefore, what's the point in imposing restrictions late at night or on Sundays when it's not financially viable to enforce?
When we design a scheme, we will issue two residents permits and one visitors permit (at no charge) but that's your lot. It doesn't mean you'll get a parting space, it doesn't mean you can park outside your house. It does mean you can park within the controlled area without getting a PCN (penalty charge notice).
As to whether you should vote yes or no, you need to ask yourself a few honest questions.
Does the number of permits they're offering suit your needs?
Is there a parking issue during the operating times of the proposed scheme?
Now here's the crunch, is the problem caused by residents or non residents? If it's caused by residents, a RPS will achieve nothing (depending n how many permits are issued)
I surveyed one recently and was impressed that the residents had the good sense to realise that most of the problem was cause because most houses had at least two cars each.
I've never known a permit be issued for a different street though. You might find several streets in a single scheme ad you can park anywhere in that scheme. If there's a scheme on your frontage, you'll get a permit for that scheme.
Hope that helps.