on the 1kz the bypass I'm referencing is built into every block. Right where the thermostat is installed. It's my understanding people block the bypass In an effort to prevent mixing and uneven heating between the cylinders between the hot head coolant/cold lower rad hose coolant and the warm block coolant.
Being it's integral to the block's design I would say there isn't much you could do about that. The engine needs that bypass flowing when the engine is below operating temp. Otherwise, I'd imagine you'd really cook a cylinder. Ideally yes, that bypass would be closed when up to temperature, but the benefits of having the thermostat relocated to the top of the engine, where it's the hottest and can provide the quickest reaction to engine temp fluctuations far outweighs the benefit of having the 'proper' bypass operation.
I gutted my stock thermostat and replaced it back into the stock factory housing. Having a bypass-only valve in this factory location would be the GOAT solution, but I've never heard of such a product.
My take would be not to worry about the bypass being open. Far more damage can be done by a true overheat of the 1KZ. If you're able to monitor the actual water temp on the engine outlet like I have mine configured, I think you'll be fine.
