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But in heavily congested and built up cities where new lines are required to carry subway loads it would be cheaper than a subway, and has to be elevated to bypass things on the ground, which means in those cities the LRT would have to be elevated also, and be able to carry such loads.
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If LRT is elevated then it can carry such loads. Capacity constraints on LRT are mainly driven by how long your trains can be, which is in turn driven by the length of streets you're crossing during at-grade operations. If there are no at-grade operations, there aren't capacity constraints.
So the question isn't whether monorail is less expensive than subway. The question is whether monorail is less expensive than elevated light rail. And it's only worth asking that question in the extremely rare occasion when your entire light rail line will be elevated, because if you want to run any at-grade or underground then you can't use monorail (or you can, but it's astronomically more expensive).
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Pretty sure they can climb grades better than LRT, which is why monorail is used rather than railed HRT in Chongqing.
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This is a legitimate use. But the ability to climb grades a little bit steeper will only be worth the trade off of not being able to run at-grade or underground anywhere in the system in a very, very few places.
In other words, monorail is a niche product that will never "arrive" as a replacement for traditional modes because it is inherently more limited. It can be appropriate if a very specific set of circumstances apply, but that's only going to happen about 1% of the time.