It's been my experience' after 20 odd years of working in singing workshops with people of varying levels of starting skills, that unless there is actual physical damage or deformity of the vocal equipment (extremely rare) that anybody can sing. Some find it harder than others - in the long run, development of the voice depends entirely on the amount of time and effort you are prepared to put in, both at the beginning and throughout the time you wish to sing.
In The Critics Group, and later in the London Singers Workshop (and various other groups), we used a series of voice developing, singing and relaxation exercises to develop and maintain the voice - they worked for those who were prepared to use them.
The danger was, if you were not careful they could become an objective in themselves rather than a means to an end.
Singing is, or should be, the passing on of emotions, ideas and information via musical sounds married to poetic texts - the voice is the means by which you do this - a collection of tools, all with specific functions which you learn to understand, control and keep in good shape so they are fit for purpose.
Not everybody is going to reach the same level of skill, but if we let this be a factor we would never do anything - you will always find someone who is better than you at whatever you try.
I have to say that I find the logic of the modern method of 'teaching singing', at the various singing weekends I have attended - the passing out of texts, teaching the tune, than singing from the sheet "parrot-fashion", totally unfathomable.
'Learning to sing' is a long-term job which, in my opinion, has to begin with becoming familiar with your voice in order that you can take control of it and push out to the boundaries you feel you want or need to.
As the feller said, the way to The Carnegie Hall or wherever is 'practice' - I don't believe there are any shortcuts.
Jim Carroll