It will be interesting to see whether anybody gives a positive answer to this question before it is closed by those who think this site should just be for IMO problems.

However, speaking as someone who abjured Excluded Middle twenty or more years ago, I would say no.

Essentially, Excluded Middle is like the fear of water. If your parents take you swimming as a baby, maybe before you can walk, then you do not develop the fear of water and learn to swim entirely naturally.

Similarly, if your teachers do not constantly indoctrinate you by beginning every proof in their lectures with "suppose not" then you will naturally grow up to be a constructive mathematician. It is only difficult because you have been told to think it is.

It is common to see arguments that use contradiction quite gratuitously.  They are much more complicated because, instead of proving $A\Rightarrow B\Rightarrow C$, they prove $\lnot C\Rightarrow\lnot B\Rightarrow\lnot A$, so the argument is back-to-front.  When some parts of a proof are written forwards and others backwards, it turns into spaghetti.

In fact (to give some mathematical substance to this reply), there is a lot of work in theoretical computer science based on the idea that the double negation rule is like a "computational effect" (such as exceptions and gotos) in programming. Unless used vary skillfully, such effects make programs next to impossible to understand.

On the other hand, there is considerable skill (that classical mathematicians refuse to acknowledge) in pulling a classical proof apart, teasing out its underlying concepts and creating a new constructive proof.

I would, for example, strongly recommend <i>Constructive Analysis</i> by Errett Bishop and Douglas Bridges, which gets on with proving the theorems without dwelling on the counterexamples.