You can make an attractive hoarse voice, if you mix your real voice and hoarse voice properly.
The attractive voice just slightly includes the hoarse voice.
If you are used to listening to the different voices of popular singers, you can understand that many professional singers open the vocal cord when they are singing. Some professional singers can even control the glottis to open or close easily and smoothly. These skills and techniques are applied to produce a great voice. The pharyngeal cavity is also important to turn the hoarse voice into a rich voice.
Note1:If all your breathing is used to vibrate the vocal cords, the sound will become too loud and possibly discomfort people. Strained vocalizing, is okay to an extent, uses a little bit of a hoarse voice only to express and accentuate various emotions.
Note2:There are two reasons why your singing is not heard well from yourself. The first reason is the most common, which is simply just lacking a sense of rhythm. Another reason could be because its too hard to, or you just can’t, control opening and closing the glottis. People who struggle to sing a song the most usually have these two issues. You have to practice and learn control in the voices’ mechanics to sing an amazing song if you want to attract or captivate your audience.
Note3:You have to touch the throat muscles to become more familiar with their current, and future statuses. Which will help in being able to identify improvements. Such as, if you want to know the obturator muscle in detail. Although keep in mind that some muscles ( e.g. the lateral cricoarytenoid muscle, the transverse arytenoid muscle and the oblique arytenoid muscle) are positioned behind the thyroid cartilage. These are used to control the opening or closing of the vocal cord, and cannot be investigated over the skin.