not true at all, you're cherry-picking situations
"If you don't show pick intent and your champ gets banned, people say "well you didn't show pick intent so it's not my fault I banned it".
that's only if:
a) it was a decent pick
b) you were likely to get it
- aka, if you were one of the first picks on your team if you were picking a high pick/ban rate champion or is was simply not a contested pick
While if you do show your pick intent and your champ gets banned, people say "well too bad".
this simply...well of course. That's just like...obvious right? There is literally no way to stop that situation from occurring and it's not any one's fault but your own for not saying who you want to play
so basically, if you are trying to get a highly contested pick as 4th / 5th or even sometimes 3rd pick, you can't expect to actually be able to play that champion and you can't expect your team to expect a highly contested champion to get through to your late-pick stage. And you also can't expect your team to just be ok with your op "pocket pick" yasuo jungle either...that's simply unfair to your team.
Also even if a highly contested champ has a 40% pick rate over a game with 2 teams, that means that there's only a 20% chance the enemy team will get him and an 80% chance that you screwed over a teammate for no reason.
that isn't correct statistics. Let's look at Syndra atm:
http://champion.gg/champion/Syndra/Middle
10.38% play rate
+
55.26% ban rate
= 65.64% total game participation rate
That 10.38% play rate is produced from the ban rate. The "% play rate taken from games where Syndra is not banned" statistic would be much higher than 10.38% , because the opportunity to play Syndra has risen while the total number of games has not.
Now to your point:
Let's go with Syndra's pick rate (taken from games where the champion is not banned) which would most likely be about 50% and assume you are last pick. That does not mean that 25% of the chance magically goes to the enemy team while you (the person that is pick intenting Syndra) make up the appointed 25% of your team. That means that out of the 9 the players that are picking before you, there is a 50% chance that Syndra will be picked before you, with the % increasing by each person that doesn't pick it.