There are quite a few DIY bird cages on YouTube that are furniture adaptations, though they tend to be built more for finches/canaries. Softbill birds tend not to chew at the wood and therefore the wood type, treatment and paint/varnish issues are less significant than for budgies. It can be difficult to clean in the wooden joints and with (usually) solid back, sides, base and roof, they can be quite dark, so would need to be placed in a well lit area.
I did consider doing this a year ago for my canary but decided against it due to the above reasons.
If you can find a way to do it safely though, they can look very attractive and it's nice to have something unique!