Q:

Problem with conversion of UI controllers' boxes to expressions

Bug introduced in V10 and partially fixed in V11.1.1

TLDR
Various of expressions which have fancy typeset form or are designed as UI elements won't survive ToExpression @* ToBoxes round-trip. And they should.
Examples

InterpolatingFunction (new)
MakeExpression[#, StandardForm] & @ ToBoxes @ Interpolation[
    {{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}}
] // Shallow

ErrorBox[ErrorBox[TagBox[<<5>>]]]

ToExpression::esntx: Could not parse TagBox[<<1>>] as input.

InputField
ToExpression @ ToBoxes @ InputField[Dynamic[x]]

 $Failed

ToExpression::notstrbox: InputFieldBox[x] is not a string or a box. ToExpression can only interpret strings or boxes as Wolfram Language input.

I don't expect InputField[Dynamic[x]] but at least something which is a proper expression, e.g. button works:
ToExpression @ ToBoxes @ Button[Dynamic[x]] // InputForm

Button[Dynamic[x], Evaluator -> None, Appearance -> Automatic, Method -> "Preemptive"]

Things get weirder, MakeExpression can handle InputField case:
InputForm @ MakeExpression[
    #,
    StandardForm
] & @ ToBoxes @ InputField[Dynamic[x]]

HoldComplete[InputField[Dynamic[x]]]

FileNameSetter
InputForm@MakeExpression[
  #,
  StandardForm
] & @ ToBoxes @ FileNameSetter[Dynamic[x]]

ErrorBox[RowBox[{"FileNameSetterBoxes", "[", ErrorBox[Dynamic[x]], ",", "Open", ",", All, "]"}]]

Syntax::sntxf: "FileNameSetterBoxes[" cannot be followed by "x,Open,All]".

Question
Are those bugs or have I missed something. Please help me understand that. :)

related
ToExpression and ToBoxes aren't inverses of each other?
How to make RawBoxes to be Expression

A:

A support case with the identification [CASE:3706792] was created.

InputField

[...] This is an issue with ToExpression. I have brought it to the attention the relevant developers and they are further investigating the issue. [...]

Bug introduced in V10 and persisting through V11.1.1
FileNameSetter

[...] the issue for FileNameSetter is different than in the other cases [...]

Bug introduced in V10 and fixed V11.1.1

