やりたい放題 is a bit different from other ○○放題. It's an idiomatic phrase which primarily refers to someone's tyrant-like, irresponsible, self-indulgent behavior. Because it usually has a negative connotation, it's less likely to serve as a marketing phrase (except something like this).
やり放題 is less common and may refer to the same thing as やりたい放題. But actually やり放題 is the word that sounds closer to "all-you-can-X" as in 飲み放題, 食べ放題, マンガ読み放題, etc. That's why you got many results from manicure salons (ネイルが○○円でやり放題) and sex-related articles. Unless properly modified (eg レトロゲームやり放題, インターネットやり放題), I personally feel やり放題 can be easily associated with sexual contexts. Please use it wisely.