I agree the full action will have more benefits!
Not really; this is by the book stuff that most follow without questioning.
Several reasons to continue what you've found more effective:
-You're focusing on the sweet spot of the movement that hits the muscle better. Every exercise has it, should be focused on. Generally the sweet spot is not at the beginning or end of the movement. Cheats and partials, techniques that often expedite development and exaggerate beneficial stress on the muscle rather than the connective tissues, follow along the same lines of theory based on mid-ROM emphasis where the muscle has better mechanical advantage. At the end and beginning of ROM the muscle is in a weak position in relation to the stress shifted to the connective tissues.
It's no accident that many pros don't use particularly strict form-they're shifting the stress away from the beginning and end points of ROM.-In each exercise there are one or more areas of the ROM that exaggerate the negative stress on joints and ligaments while having minimal beneficial effects on the tissue-the exact opposite of what you want. In your case the bottom of the BP ROM; you've already noticed this in mentioning that including this is not effective for your chest. While it's possible that your form may be to blame, the more reasonable assumption is that your body's telling you something useful that shouldn't be ignored. For others, the same applies to dips and for most, the bottom of preacher curls & squats, which should be avoided.
-Constant tension-you're likely making fuller use of it by stopping short.
Try going all the way down but if you find the same effects-too much shoulder, too much potential strain on the joints, do not continue. Rather,
continue with what works, baby.Also try partial and full range ROM with DBs as well.