I agree with Pika Fox that items ALONE do not change the outcome of the game as there are other RNG variables to take into account like champions offered, if a certain comp perk procs (e.g. demons, gunslinger, ranger, yordle etc).
I really don't think all players should be given the exact same amount of items though. I feel like that would take away the chance for a player who got given bad champion options to still have some hope. Although I understand this can work in conjunction with other bad RNG to create a game that feels unwinnable, it can also do the opposite and work with good RNG where a player has great champion picks and many items to facilitate a win. And I think that's fine.
TFT is a game-mode where you've got to be extremely flexible, think miles ahead and even be ready to sell your entire team to change comp if your comp is countered by another or just to transition successfully. (now I personally can't do these things I am a very stubborn rigid player but somehow it works ok for now).
I think normalising the amount of items drops per players would make the game-mode more boring, as it will become more predictable and too much predictability simply means less surprises which leads to more boredom.
Yes it can be annoying when you're on the receiving end of bad RNG but you're just as likely to be on the receiving end of good RNG (this is relatively simple math if anyone wants to provide mathematical proof).
I just take it like I take normal games of League: 20% of the time there is nothing I will be able to do (due to other players or bad RNG) and I will lose the game for sure, 20% of the time whatever I do it's probably a win (due to other player or good RNG) even if I make many mistakes, 60% of the time the win or the lose will be dependent on me and the choices I make etc.
That way, when I overwhelmingly lose it helps to lessen the loss knowing there are times when I will overwhelmingly win effortlessly.
Now if you feel like you're always on the bad side of RNG and barely ever on the good side of RNG then you have to change the way you think because it is simple math, after just a few games it is possible you have been dealt a bad hand, but after enough games there is no way you've been more often dealt a bad hand than a god one. If you think this is the case (and I don't say this to insult anyone I've been there too) you may be shifting the blame from your skill level to RNG a bit too often because probability states otherwise.
I think riot has made a great step towards lessening the effects of item number differences between players by adding possible gold rewards instead of items.