The question (including the comment) has some misconceptions or misstatements, regarding Devanagari. Almost every Devanagari letter has a correspondence to some IAST letters. The Devanagari letter त corresponds to IAST "ta" (a sequence); the Devanagari letter sequence त् corresponds to IAST "t"; the Devanagari letter क्ष corresponds to the triple sequence "kṣa". Also, if one counts "diacritics" as separate letters (e.g. Devanagari vowels, also nukta), then IAST "ṭa" is a three-letter sequence, "ḍha" is four letters, corresponding to one Devanagari letter.
A simple translation from IAST to IPA is possible, but not the reverse, for example there is no IAST convention for representing [æ, ɨ, ħ, χ, ɜ, f...]. Everything that can be represented in IAST maps to something in IPA, in that sense IPA is compatible with IAST and Devanagari.
No system "represents all human language sounds", but IPA and the Americanist systems can represent all known phonemic distinctions of human languages (UPA does not purport to cover all language phonemes, for example it has no pharyngeals). Micro-transcription with positional-variant transcriptions are possible in both IPA and the Americanist traditions, but IPA has more of them so it is better able to indicate finer distinctions (comparisons across languages and low-level phonetic distinctions).