Talk about the practical benefits you can get, and decide based off of those:

- GET requests are supposed to be idempotent so they can be transparently cached by caching proxies. Even if you won't be taking advantage of caching proxies, it makes it easier if you can use the same data and mechanisms (i.e., HTTP headers) for server-side caching (and makes it easier to pull it out onto a separate server later). This is important if it gets a bunch of traffic or requests are resource intensive.

- Thinking about endpoints as "resources" instead of as function calls discourages you having parameters with a large or infinite set of possible inhabitants, which would dilute your cache utilization. "mysite.com/multiplicationTable.html" is nicely cacheable; You can cache "mysite.com/mult?a=5&b=10" if you want to, but how likely is someone to request that same URL again before it falls out of cache? Any information that changes the response is technically a parameter, too (since it invalidates your cache) - that especially means things like session state and side effects. That doesn't necessarily mean "never have side-effecty/RPC endpoints", but you should minimize them if you want to be scalable, since every request to one pretty much has to put load on your server.

- PUT/DELETE requests are supposed to be idempotent so they can be re-issued in case of failure. I also find it encourages design with immutable/replace semantics, rather than partial update semantics, which puts you in a better position when you want to move toward distributed/eventual consistency systems (or even just for debugging), since the data's all there in the request, and likely easier to make it commutative with other requests. Some of these things might matter to you more than others, depending on what you're building.

- Using headers properly gets you nice features like content negotiation, and provides what's needed for caching to work (e.g., 'vary' header). Using the built-in stuff means you can probably use someone else's library instead of hacking out something buggy yourself.

- HATEOAS gets you fully dynamic API discoverability. Describing your links well enough to accomplish this is pretty involved, and I'm personally not really sure it's worth the benefits, at least for anything that isn't an API having arbitrary clients built for it, or otherwise being directly navigated by some unknown end user. Maybe if there were more standardization around hypertext formats.

- Proper error codes can be nice for debugging, and theoretically can let certain situations be handled automatically (e.g., 401s could direct a user to authenticate, 302s generally redirect transparently) They also communicate some intent to e.g., search engines ("pass on my SEO link juice to this new URL"). They're a bit of a harder sell for internal APIs, since they're not really as descriptive as they should be. Probably the best practical benefit would be the ability to use client- and server-side libraries with them, or to be able to categorize your errors easily to simplify your handling, without having to dig into the response body. Also nice that you can look them up on Wikipedia - you don't have to maintain documentation for your own error format.

TL;DR: sticking to HTTP as intended helps to save you from rolling your own cache invalidation and coming up with your own new names for things, which are well known to be the two hard things in Computer Science.