Depending on your organization (e.g. size, industry, structure, etc) there are various challenges while implementing ITIL - costs of the implementation (e.g. tools, time of internal resources or consultants, etc.), whether IT Service Management tool is in place, knowledge...are just some of them.
Some can remain once the implementation is over (e.g. costs of external/internal resources or quality of implemented ITSM tool), but there are some other as well - how efficient your ITIL processes are (or how complex they are), related (human) resources and quality (as well as know-how) of their work, support of your management, etc.
Here are more details 5 excuses why IT organizations avoid ITIL implementation https://advisera.com/20000academy/blog/2015/08/25/5-excuses-why-it-organizations-avoid-itil-implementation/