I live within 20 minutes of 3 dealerships in Sydney. But regardless of access to the dealerships, the issues my triumph riding mates and I had was always parts being on Back order. Things like, the regulator rectifier, which used to plague triumphs. (I'm hoping they are all sorted now) They all blew up. Within a few months of each other and it was after the warranty period.
Regardless, they had to back order them. It was going to take a few weeks, so we just modified an R1 unit for it. What sucked was the time it took them to get parts from the UK or Thailand.
But of course, the dealer had most of the maintenance parts ready to go. Oils and filters. Sprokets and chains had to be ordered. Clutch cables, etc. I guess it depends on the popularity of the bike wherever you are. I'm in Sydney and they are quite popular here. Bearings, sprockets, and other parts that are not shared with other bikes took a while since they had to be ordered in. ALSO, I found it hard to buy these types of parts from after market vendors. I had to buy Triumph brand ie. Expensive.
I liked working on bikes myself. The triumph wasn't complicated. But I had to plan well ahead to make sure I had parts.
The main reasons I bought the GSXS over the other super nakeds are:
Price, Performance (Pretty much on par with the rest of them based on the way I ride. Communing and mountain stuff), Parts and maintenance can be easily done by yourself easily and affordably, and as you know info on the K5 is everywhere. Pretty much all bike shops have worked on Suzukis and have the parts right there since it is shared across so many models. Ebay parts are cheap and plentiful.
Reliability. I have mates with K5-K8 bikes going on 100,000km. No issues if fluids are changed regularly. Suspension and brakes are from the newer GSXRs, etc.
I bought the bike very well that, there is this an issue with throttle snatch. I test rode the bike and it had throttle snatch. I used that reason to get a further discount

However, I knew that there is a way to fix it. And, if you read the TPS thread, it's a 5 minute free fix you can do on your home.
Stock exhaust sounds amazing as is.
You will also need to get a single sided swing arm stand for the speed triple.
At the end of the day , it's an emotional buy right. But the Suzuki won out because it is also super easy to live with.
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What parts did you need to order? Were they common items, accessories, or uncommonly replaced pieces?
Do you know if the trouble getting them was due to the specific dealer or their supplier? I have a Triumph dealership a few miles away from me and their US headquarters is an hour drive.
The availability of Suzuki parts and service centers is certainly a bonus. Plus, a lot more people know a lot more Suzuki than they do Triumph.