Addressing the "I went in because you were taking too long"
Well as our as our sole initiator and tank, I do need to find an opening and sometimes there just aren't even half decent/ideal opportunities as of yet, most times there is absolutely no reason to force a poor engage unless it's something crucial like Baron, Elder Dragon or a game ending siege. As 
I have 1 tool of initiation apart from flash and if I miss then we just have to wait until it's back up, but engaging as a squishy into a team of 5 champions is certainly on my list of one of the easiest ways to lose a game effortlessly, and honestly it's just absurd to blame the tank for not "just" initiating earlier instead of just waiting.
Champions like 
make or break team fights depending on their initiation and how many they can affect with their AOE initiation, so even if you see an ADC they could ult or a juicy carry, sometimes just 1 carry isn't worth it when they could potentially get the entire back line CC'd instead.
So please to all the 
that engage by themselves because they're really anxious to fight for no reason please don't blame others for your inability to wait for the tank to engage first and instead engaging by yourself to die instantly usually leading to a 5v4, loss of objectives or even more likely the loss of the game if done after the 30 minute mark.
I know there are times when squishes can engage and see an opportunity, but the majority of the time you will instantly die with absolutely no reward so please I implore you to just be patient and wait instead. As a carry you're more than likely a huge part of the teams damage and when combod with CC will be absolutely devastating with little counterplay.
Example Ideal initiation situations for a single point initiators(AKA GO in hard and live or die with your decision cause there is no turning back) like
Super Ideal: Bandage toss onto an enemy carry and (flash) ultimate entire back line/ Bandage toss onto anyone into a 4-5 man ultimate. Ideal: Bandage toss onto anyone + 3-4 man ultimate/Bandage toss onto carry and ultimate carry + 1 (depending on how fed said carry is just chain ccing/nuking them can be very worth it)
So if you realize that at no point is there a situation in which it's ideal for your tank to engage then if you can wait for a better opportunity do so. There will always be a point at which the enemy team will slip up and mis position allowing for a great engage but it's just a matter of being patient. In regards to poke comps then I would advise you ask your initiator to engage ASAP since you want to engage before they reduce your health but please don't for the love of Shurima enagage prematurely as a damn squishy.
Regards
A Vanguard Main
into the enemy team, I really hate you.