You can’t sing fully if your voice isn’t strong. Yelling is not a good way to develop true vocal strength.
Loudness alone is not a sign of enduring, sustained strength. Strong voices can be loud, or not. A strong voice can do things a weak voice just can’t manage.
A strong voice can handle a lot of exhalation pressure without being breathy (due to firm closure of the vocal folds) and a strong voice can express a great deal of powerful emotion without being overwhelmed. A strong voice can get quiet easily without falling apart.
Generally one can’t develop full energized vocal strength without training. Strength is what allows a voice to be undistorted, unconstricted and unmanipulated. It is rare that such strength can be cultivated by self-training alone. Natural talent can take a person a long way, but it will never do what training does. Training makes up for the lacks that are inherent in all voices. Just as someone who is a very good, coordinated natural dancer is not capable of being a prima ballerina without years of diligent training, someone with a nice voice who is a good natural singer, who has had no formal vocal training, will never be capable of doing the things that someone with years of training does.
And, someone with a great deal of training may not sound like they have training, which, in a certain way, is the point. They might have certain vocal skills but only use them when they choose to, and at other times, keep them “under cover”.
A well-trained cultivated voice has many characteristics. What are they? You would be surprised to know that many people, even those who teach, have no clue.
A well-trained cultivated voice spans at least an octave and a half, but more likely at least two octaves. It can be that it covers more than three, or maybe even four. It can go from pianissimo to fortissimo through at least 3/4 of that range. It produces undistorted OR modified vowels (as needed) and clear consonants. It has (or can have) even vibrato or produce a straight tone (as needed). It can also be breathy or nasal for expressive purposes (as needed in some styles). It is recognizable as being itself (unique) but is consistent, even and under control, all the while being free (not constricted or strained). It is generally pleasant but can make “unpleasant” sounds (as needed). It is not consistently distorted, swallowed, strangled, nasal, harsh, caught, pinched, stiff, grating, muddy or any of a thousand other not nice descriptions. It expresses true, deeply felt emotion without unnecessary effort and it handles various kinds of stressors (that means mild illness, environmental disturbances, and professional demands) without undue problems under most circumstances. The vocalist does not need to make any strange faces or movements, aside from moving the mouth, jaw and face. And, the person singing belongs to, likes and is happy with the sound.
It may also be that the voice can sing comfortably in many styles. That is an asset, not a requirement.
I have not ever met anyone in almost 40 years of teaching singing who could do all of these things equally and easily without training. The list above does not include any of the other factors that a trained voice is supposed to handle that have to do with performance such as knowing how to do ornaments, melismas, colorations, and things that require musical virtuosity like rapid scales, staccati, arpeggios, crescendo to descrescendo, etc. It does not include linguistic things, or factors involving the use of microphones and amplifiers, or being on a stage in various kinds of venues. There are many things that are not included that have an impact on vocal capacity and ability that are not, on their own, vocal skills, but they matter, too.
You can sing and have a career if your voice doesn’t fit into this description and you can, of course, be a very good vocalist without having all these capabilities. That is a different subject. Singing does not fit into only one box, but, if you do not understand the purpose of training (and many people do not) you certainly cannot understand why, regardless of what you want to do with your voice (including professional speech), it would be necessary.
Many years ago, while I was still in high school, my mother attended a social function at which she sat near another woman whom she did not know. They ended up speaking, as mothers do, about their daughters. My mother was very proud that my father was paying for expensive singing lessons (a true sacrifice on their part). When the topic of singing came up my mother mentioned that I was studying singing. The other woman replied “Oh, that’s too bad. My daughter is so good she doesn’t need training”. My mother just smiled.