Yes femmeayfoyer, there is no obligation to register the birth of a child of a British citizen and in most cases it is of no consequence and no need for proving British citizenship. IF you're British by birth and not descent or naturalisation, then your child born in France will be British by descent and will not pass on British nationality unless he/she has a child born in the UK or who moves to the UK. Exceptions are diplomats/special ID/Armed Forces who are treated as if they are giving birth in the UK - this certificate of registration with a British Consulate shows the status of parents at time of birth so "British by birth" and not descent can continue.
RichManPoorManBeggarmanThief has a good reason for registering - in order to provide a 2nd means of proof of birth for someone in HKG in case China one day decide not to issue copies of that birth.
Doradoo has a complicated reason for needing to do the registration, connected with Armed Forces if I understand correctly.
For the vast majority of cases, you gain nothing from registering the birth at the nearest British consulate. Nationality is NOT the result of this piece of paper. You are correct, the French birth certificate is your means of proving place of birth, not the British Consulate document.
Getting a British passport is not a faff at all really, really it isn't, no more abroad than in the UK. All UK passports are now issued by IPS, no longer FCO. There are upsides and downsides to both the old system and new. It just might take a bit longer from abroad and definitely costs a lot more. Most of our passports are bought in the UK on "visits"! Hubby's latest one couldn't be due to time constraints so it came via Paris via somewhere else in the UK. First passport issues always take longer, renewals should be straightforward - saying that we had 1 turned down for renewal because suddenly someone wanted to see proof of marital status which had already been proved on first issue, stupid person had to be reminded of that!!!! AAAAArrrgh. It was frustrating, given our actual jobs abroad. Also got turned down for a British ID card (shortlived exercise) because high ranking UK civil servant who had countersigned the photo was turned down as a reputable countersignatory which she was rather !!!!!!!!! about given her status, bloody lost our money over that along with 1000ssss of other British citizens, as Cameron halted the issues and IPS swallowed up ££££££ of British citizens' monies in refusing to refund application fees. Rant over.