Here’s a good example of why we split infinitives in English:
You may have heard that it’s bad grammar to split an infinitive. This is a made up rule that was taken directly from Latin. Thankfully, it seems to have been buried for good as people are starting to realize it’s a ridiculous rule. The infinitive is already split in English – there’s always a space between to and the verb. And you can see here that following the rule would produce some really weird sentences:
I wonder what it feels like to be not tired.
I wonder what it feels like not to be tired.
Both of those sound unnatural and unindiomatic.