I would like to create a custom UITableViewCell which displays some date and shows a UIDatePicker as keyboard when selected.
While I found several topics dealing with this question they all offer the same solution: Add a UITextField to the cell and set the UIDatepPicker as inputView of this TextField.
This solution works fine but I do not like it. It is quite hacky and it should not be necessary use a TextField if no text should be edited. All I need is a label showing the data and a DatePicker keyboard to change this date.
What I tried:
Diving a little deeper I found out that UITableViewCell has its own inputView property which it inherits from UIResponder. However, I cannot override (Cannot override with a stored property 'inputView') or assign this property (Cannot assign to property: 'inputView' is a get-only property). The same is true for canBecomeFirstResponder and other properties which would have to implemented / changed in order to let the cell work firstResponder / inputView.
I wonder how UITextField is implemented since this is also a UIResponder subclass.
Long story short:
Is it possible to create my own UIView (or even better UITableViewCell) subclass which acts as a kind of input view and shows a custom keyboard?
Or is using a (hidden) TextField really the best solution?

As already mentioned in a comment there is nothing "hacky" about it. This is a standard procedure. Although your input view may look like a label or a button it is still by all means an input field which opens a dialog similar to keyboard which uses a date picker.
But if you are really into not-using-this then there are several alternatives. I assume that when a cell (or a part of it) is pressed then a date picker should appear somewhere. Well then the answer is pretty straight forward; create an even which will trigger when the region is pressed. You can use a button, you could use a table view cell delegate to check when row is pressed or you could even add a gesture recognizer if you think it suits you better.
In any case once you have an event you can present your date picker anywhere you want. This can be presenting a new window or putting it in your view controller or even in your table view if you like.
But whatever you customize will negate the native logic off iOS devices which may bother some users. For instance if you don't make exactly the same animation when picker shows it might look weird to users that are used to having things the way they are natively.
Or maybe you can do it much nicer than native in which case go for it. But note you may have quite a task to accomplish. Animations, touch events, dismissing date picker, repositioning your table view so that date picker does not overlap your cell...