In Japan, most homes have automatic baths which set up the bath at a pre-set temperature and pre-set level. However twice I stayed at high priced hotels and the room bath was a manual bath like you commonly see in the western countries in private homes and its a real pain- difficult to set to a temperature and wasteful as they have in-bath drains which often drain when you get in because its set to 2/3 of the bath depth. Hence I ask if its standard to have make own baths in Japanese hotels? And why? My last stay was in resort in Okinawa- the most expensive hotel in the south of the island and the previous stay was in a ryokan in Kamogawa which is on the far side (to Tokyo) on the mainland.
Bathtubs of any kind aren't actually all that common in Japanese hotels. The cheaper ones, especially business hotels and the like, tend to have only showers, and most minshuku/ryokan and all capsule hotels don't have any in-room bathing facilities at all, only large communal and/or reservable onsen baths.
If you're staying in branded Western chain hotels, though, you'll probably get the Western-style bathtub, because that's what non-Japanese clientele expect: a room in a Hilton in Tokyo isn't too different from one in New York. Even Japanese-operated luxury hotels (random example: Okura Huis Ten Bosch) will often feature these, because like the faux-French furniture in the room and the exorbitantly priced Italian restaurant downstairs, they're a bit foreign and exotic.
The one place I have seen the home-style fully automated deep ofuro baths is apartment hotels intended for longer stays, like the Tokyu Stay chain. Which makes sense: these are designed as a replacement for a Japanese home, so they have to offer the facilities of a Japanese home.
If you want to have a Japanese bathtub, it's best to stay in a Japanese-style hotel!
Yes, Western-style hotels and business hotels generally have more western bathtubs. Remember, in Japan, baths are for bathing, not washing. In general, showers are better at washing your body.
Many Japanese consider it gross to sit in a bathtub of your own body's dirtwater and will either shower after or before starting a bath-tub anyhow. Some hotels will have a Sento (public bathing area) which is much preferable for many Japanese anyhow. If you've been to a Japanese home, you'll know that toilets and baths are separate rooms and bathrooms are usually wetrooms with a shower unit outside the bath. These are fantastic but can take up more room and are more expensive to construct. As such, hotels generally use Western baths.
The MOST expensive hotels in Japan are usually built on an onsen (hot spring) or at LEAST have a nice Sento, a much more preferable arrangement for actual bathing.
If your clientelle is mostly just needing to wash, then western shower-tubs are preferable... which is why even expensive hotels are decked out western-style.