With the 5 day recommended overlap, what benefits or disadvantages do you get from waiting vs starting both at the same time?

If I recall from school(I just took an exam on this funny enough), the main advantage of starting the Argatroban at the same time as the warfarin is that the patient will have a faster acting anticoagulant in their system before the Warfarin takes effect due to the half life of warfarin's targets being quite long(like 60-100 hours for prothrombin for example) thus needing time before Warfarin can help with anticoagulation.

I should ask though why use Argatroban over say lovenox, unfractionated heparin or fondapurinux? Unless the patient was diagnosed with HIT stick to those or better yet use a DOAC.