1. At the core, lithium-ion batteries are expensive per WHr. There is no getting around this. Lower bound is around 50 cents per WHr for an assembled pack, retail pricing. So for 1000 WHr which is what I would consider to be just good enough to actually go places and do things at speeds that are competitive with car travel. So that's around 500 dollars alone in the battery pack.
2. Good motors are ultimately still a lot of money. A G510.1000 from Bafang is what I would consider right around what is actually useful. So call it 600 dollars for the motor, throttle, display, etc...
3. A bike for the base will end up being somewhere around 1500 USD street price, especially if you want full suspension and components that aren't Walmart bike tier where the fork is downright dangerous, brakes that don't work properly, derailleurs that take forever to shift, etc.
4. Add 25% because of the US tariffs.
You're at 3.3k and this doesn't even include customer support, a warranty, or anything really. Let's be kind and say the model is direct to consumer with no middlemen and we only do remote support and leave LBS labor charges to the consumer. 3800 USD is around what you get.
Is the BOM cheaper? Yes. Are you actually going to get that price? I'm very doubtful about that. And before you say that the ~15% margin the ebike OEM makes is excessive, that's the price you pay for being able to actually do things like chargebacks if their support violates their warranty terms.
I will say though this makes certain assumptions like you don't want a carbon fiber frame, you don't want super high end bike components, etc. You can easily make a bike that costs 7-8k before electrification if you start going down that path.