People seem to miss that part where these teams are highly organized and plan comps around these picks to bring out their full (or at least increased) potential. I want to kick the idiot who picks ezreal mid in solo queue because they clearly don't understand what makes it work. They just see 'pro do thing. I do thing. I be pro' and do it.
Here's the thing. There are champs are that just strong.
Nunu for example, is way too strong. Nunu didn't really get any direct buffs, but the increased jungle respawn timers and emphasis on dragon control puts the game in a place that suits him much better than it should.
Urgot is strong in LCS because the teams understand what they sacrifice by picking him and what they need to do to make up those weaknesses, or compound the strengths. Urgot is very low damage compared to the ADC or mid laner he replaces, so the damage has to be made up elsewhere.
<Insert AD mid here> is very strong generally, but fails quite often because picking them mid means that no one will make up the lack of magic damage. This is because people care more about their picks than the team as a whole.
Amumu is very strong is solo queue because of his potential to win engages with his ult, but is susceptible to counterjungling. Pro teams will exploit this weakness, so you don't see amumu in LCS. Katarina is the same way, just, replace counterjungling with cc.
Basically, champs that require actual consideration for their team comps are likely to do poorly in solo queue., but well in LCS. Champs that are hard to exploit without moderate organization are strong in solo queue, but can often be dismantled in LCS. Champs that are just overpowered will have high win rates in solo queue, and be picked in LCS.