The same space between notes

Notes are being places in different distances as per their duration (not quite double the distance for double the duration, but proportional), this does make scores more readable.The above antique example shows this quite clearly, it is basically unreadable. Your example though is readable. Because if the varying distances.
And no, MuseScore does not provide any automatic means of not having it that way.
For Choral notes there's another factor that influences the spacing thought: the lyrics, esp. long syllables.

As others have said, It's definitely not easier to if you eliminate these important visual cues as to duration. It's an essential part of how we process written music subconsciously, and there's a reason why it is the universal norm to space notes according to duration.

But also as mentioned, in choral music, the lyrics too will affect spacing, the space between shorter notes is automatically increased as necessary to accommodate lyrics.

So again, unless you are designing your own experimental notation, please do not go out of your way to force non-standard notation - it will absolutely make it harder for others to read.

That said, should you ever go into the business of designing your own experimental notations, the suggestions I gave previously as to how this can be done would still apply.

I copied your Example.png into MuseScore to show the comparative proportionality as measures get compressed.
As you compare I to IV, perhaps IV might be more to your liking;

Even though all the examples above are not spaced equally, there is much less 'emptiness' between the notes of IV compared to I. However, there is still a variable, but successively smaller, distance between the notes in each line of music.
Indeed, the tighter spacing may even seem to approach equality as the measures crowd together from I to IV.

Here's the MuseScore file:
Note_Spacing.mscz

Also, as mentioned earlier, adding lyrics can impact note spacing.

Regards.