whendidyoulast, you've already mentioned 2 of the things that would make my DCs (primary) school better ... email and parents' online chat.
Neither of those things will happen until we have a new Head though, as the current Head doesn't embrace modern communication. The teachers have email addresses, but they're not given out. You can email the school via the office, and it does get passed on to the Head, and sometimes she acts on it, but you never get a reply or acknowledgement. Instead, she stands at the school gate a couple of mornings a week to make herself 'available' to parents who want a word, but lots of parents are too intimidated to approach her in that setting.
If you want to chat to your child's class teacher you need to catch them at the end of the day at pick-up time (if they're not already monopolised by other parents, and assuming you don't want privacy). Of course you can make an appointment to see a teacher if its something major, but that's not always convenient to do (again its at the end of the day usually, so you'd need childcare cover).
Email communication would be much more convenient, and better for those people who find it hard to articulate things, and easier to write them down; perhaps because they have something awkward to say and want to phrase it carefully, or because they have English as their second language and need help with interpretation. It would also help those who work and have nannies/childminders to cover the school run.
The parents' online chat is another area that would help those who sometimes feel 'excluded' at the school gate ... non-native English speakers, working parents, those who are just a little shy, or people like me who have a hearing problem and find it difficult to join in group-chat in noisy environments.
Somebody did once suggest a parents' Facebook group, but the idea was well and truly squashed by both the PTA (who thought it might 'replace' their social activities, or exclude people who didn't have a Facebook account) and the Headteacher (who was worried she would need to moderate it). In my view it would promote inclusion.