ITIL was developed in coordination with and pushed by the UK government. That alone makes me balk.
But Wikipedia has a far better list of criticisms.
I'd say putting ITIL in the same phrase as Agile is even an insult to Agile, possibly Six Sigma as well. ITIL literally lacks implements entirely. Don't get me started.
In my experience, ITIL is really a way for non-IT people to control the process, which real stakeholders (like actual, government management) then pawns off to yet more contractors. I.e., not even technology professionals, but yet other professionals to manage those technology professionals. Which then goes back to this whole non-sense of adding yet more government contractors from private industry, instead of having competent, government staff -- technology and management.
A very 'short-lived,' early Obama administration 'Tech Czar' had the audacity of suggesting the US federal government offer direct, FTE, government jobs to contractors, instead of paying private contracting and technology companies, saving the tax payer a great amount of money. He was ousted rather quickly by special interest by, of and in NoVA (Northern Virginia) corporations, also the richest county in the entire US. I think he survived even less time than the mid-'00s Microsoft CTO who openly admitted no version of Windows was ever designed for the Internet, but I could be wrong.