He can't handle all of the taxes on his end. You still owe tax on whatever income you receive from selling on Amazon. Maybe you're selling at a low enough level where that income can fly under the radar, but if there is money flowing into your accounts whether through Paypal F&F, Paypal goods & services, ACH, wire transfer, deposit, etc., the IRS considers that income and expects you to report it and pay tax on it.
As to your original question, in addition to the question above about the value of your time, whether or not to get your own account depends on what your plans for the future are. If you're only wanting to sell a little bit of inventory here and there, your current arrangement may make sense. However, if you plan on growing your sales and trying to generate real money from selling on Amazon, I would definitely recommend getting your own account and handling things yourself. If you are selling through someone else, you have given up control over pretty important aspects of your business and placed your fate, to one degree or another, in the hands of someone else. If that person doesn't follow your directions and prices things too low, you lose money. If that person screws something important up, you lose money. If that person decides that something is more important than selling your inventory, you lose money. If that person decides not to pay you, what recourse would you have to get your money? Etc. Etc. If you are going to sell through someone else, I would make absolutely certain that you can trust that person to follow through on whatever arrangement you have with them.