Are 「〜のは欲しい」 and 「〜のは出来る」 valid alternatives to 「〜たい」and 「られる」conjugations for desire and potential form? If so, what's the difference?
Examples: If 見れる means "can see," does 見るのは出来る mean the same? If so, is there a difference in nuance?
No. However, you can rephrase 見れる as 見ることができる, and substitute の for こと like 聞くことはできない。しかし、見るのはできる, though I'd not necessarily recommend that method. In addition, presence or absence of は makes difference.
As for the difference between ～のは欲しい, for example, そうじするのは欲しい means "I want one to clean up", opposed 掃除したい, which is "I want to clean up".