I carried out an unscientific survey. But I believe my general conclusions are about right.
I selected at random 60 songs that have stood the test of time - tunes such as Tea for Two and I Can't Give You Anything But Love and It Had To Be You. I then noted the chord with which they start. I am referring to the first chord of the first bar of the Chorus (i.e., omitting any anacrusis).
Five of the tunes turned out to be in minor keys. That's just 8% of the total. These tunes certainly had a 'minor' feel but this did not necessarily make them sad.
I am going to give my attention to the other 92% - those in major keys.
Of these, no fewer than 50 tunes (that's a whopping 83% of all the tunes I looked at) started on the major chord of the tune's key. A tune in the key of F, for example, would start on the chord of F major.
I found the effect of this is to establish firmly and clearly where we are: there's no attempt at subtlety.
Of these 50 tunes, I categorised 38 as bright and cheerful in character, which means about 63% of all popular tunes are likely to be bright, cheerful, un-challenging and starting on the major chord of the home key.
The figure is about what I would have expected; and probably you would too.
But this leaves twelve tunes (20% of all I studied) that begin on the major chord of the home key but are more subtle and complex, perhaps with elements of sadness, nostalgia or melancholy. These include such tunes as I'm In The Mood For Love, Smoke Gets In Your Eyes and I'm Getting Sentimental Over You. If you look at the inner workings of these tunes you find minor chords, diminished chords and other surprises (such as a 7th based on the flattened third note of the scale in I'm In The Mood For Love). These chords make the tunes harder to learn but they also give the songs their distinctive colours and make them linger in our minds, it seems to me.
The only tunes from my original 60 not yet mentioned are five in major keys that do not start on the chord of the major key, so that's just 8% of the total. Four of these are 'bright' tunes, the other one less so. These tunes do not seem to lose any impact as a result of not starting on the key chord. Usually they begin on the Dominant 7th, and very quickly inform our ear of the key we are in. An example is (The Bells Are Ringing) For Me And My Girl.
To sum up my main findings:
83% of popular songs are in major keys and begin on the major chord of the home key.
8% of popular songs are in minor keys.
(Note: all percentages are rounded to the nearest whole number.)