It seems very irresponsible to me to not look at hormone levels prior to starting the HRT (especially if the blood is already being drawn for other tests). Suppose the patient has an undiagnosed intersex condition, and is hypogonadal? If there's pre-existing hypogonadism, good medical practice would be to properly evaluate the patient to establish the cause (and make sure it's not due to a pituitary tumor or something), and also make sure there aren't other conditions present as a result of the hypogonadism (such as osteoporosis, diabetes or heart disease). Skipping this entire step doesn't seem like good medicine to me.
Aside from that, one thing I can think of immediately in MTF trans HRT, is that the preexisting testosterone level is very important in deciding whether it's necessary to give antiandrogens or not. If the person is already hypogonadal, then there's a good chance that once they start on estradiol, their remaining T production will collapse altogether even without antiandrogens, and so the use of these potentially quite harmful medicines can be avoided altogether. Also, if a person has been hypogonadal for a long time prior to starting on HRT, they're at increased risk for osteoporosis, which makes it important that, post-HRT, their estradiol levels are kept well within the normal female range and not allowed to fall too far.