None of my mobile phone apps look like any of my other mobile phone apps.
I've never really considered it to be a problem. The thing that looks like a play button makes the media start, the square makes the media stop. The speech bubble looking thing makes some sort of conversation happen, and the photo looking icon either opens a camera or lets me add a photo from my camera roll. That last one gets a bit annoying.
But I seriously don't care. So long as every app is consistent with itself. The number of apps that follow "platform guidelines" is astonishingly small, typically those from the OS creator (Google or Apple) and people who used the sample template and who didn't bother to customize anything.
Which is another thing, if an app looks too much like other apps, it looks cheap. Sure I want proper back button and keyboard integration (numeric inputs should use the numeric keyboard and so forth), but apps that look like they fell out of a sample catalog don't feel premium.
There isn't a consistent "this is how all retail stores are decorated" standard, there isn't a set of mandated "this is how all grocery stores are laid out" regulations, why in the world do people go around insisting that all apps should look the same?
Sure, use the default platform picker if it is appropriate, but if it isn't (and finding the year picker on the Android date picker is darn nearly an easter egg, and Android's keyboard entry for time is also not up to snuff), then use something else!
I give 0 cares if an app has properly rounded text inputs. What makes an app feel good is nice animations, no stutter performance, quick load times, and a self-consistent look and feel.