I live in Australia, where diesel 80 series landcruisers (and other rigs) were common and the local dealers handle parts for them all the time. Even so, of the hundreds of new parts I've ordered, I've imported nearly all of them from overseas, specifically partsouq. Why? Not only is partsouq almost always dramatically cheaper, I've had packages from them arrive within 3 days, delivered to my door. Everything has always arrived within a week. I've done this dozens of times. This may not sound impressive by US postal standards, but I'll point out that it'd take about 3 days on average to post something to my neighbour here. If I walk into the local dealer, and they need to request parts from the warehouse in the same city (which they always do, since they're a relatively small dealer), they only get parts shipped in on Tuesdays and Thursdays, so I'm waiting 3-4 days often from them anyway. That's once I deal with a day's round trip for the email order, or go to the hassle of driving in there, then drive in there to pick them up once they do arrive. Simply put, I get parts quicker and easier from overseas than locally. And much, much cheaper.
Now, partsouq is exceptional. If you have to go amayama, be aware that the average delivery time from them is around 1 month from what I've seen. Also, if you're looking at a part on amayama that isn't in stock at partsouq, there's a chance it's actually NLA and amayama will only find out about it after you place your order. Not always, but sometimes this happens. My basic parts ordering strategy goes: partsouq, amayama, megazip, dealer, in that order.
The only time I go local is for large parts where shipping blows out. Even then, it's often cheaper to pay the shipping cost. I'm getting a new rear prop shaft for my 80. Cost from partsouq? $599, plus $200 for delivery. Cost from the dealer? Over $2k. I'll pay the delivery charge, and buy a few other large parts at the same time because then the extra shipping weight/bulk is pretty much free.