I used to do a much higher mileage than that. I never cleaned my chains and I rarely lubricated them either. I never had to replace a chain nor a sprocket. The bikes did around 2000 miles each before they were replaced with the next project. My present bike has done 6000 miles, and I replaced the chain once.
As I said, I oil the chain using hypoid 90 gear oil when it starts to sound rough, which will be after whenever I ride it in the rain, otherwise about once a month or two. I use the cheapest chains, so it's not worth doing any more than that, i.e. total chain cost in 5 years and 6000 miles is £8.
My hub-motor is similar to yours, so you should expect similar to what I get.
You have to remember that bike shops make their money out of selling stuff. You take your bike in because the shifting isn’t right. Normally, it can be fixed by simple adjustments that take minutes to do, but I guarantee that they'll tell you that you need a new chain and cassette plus fitting cost. If you challenge them, they'll put a chain gauge on the chain, but I almost guarantee that if you've used any chain for a week, it'll fail the test. Likewise, they'll point out the shark's teeth on your cassette, conveniently forgetting to mention that they're supposed to be like that.
Everybody has their favourite way of looking after their chain. When I had a motorbike, I bought two new chains for it. Every 500 miles I swapped them, cleaned the one I took off by soaking and shaking in parafin, then I boiled it in the chain grease to make it ready for the next change. That made zero measurable difference to the life of the chains or sprockets compared with an odd squirt of hypoid 90.
Maybe if you have hideously expensive sprockets and chain, it might be worth it, but for what you have, it isn't.
