Because we don't! In spite of its large proportion of Latin vocabulary, English nearly always gives us a choice of a Latin or Germanic phrasing. And for everyday use and everyday actions ,we generally prefer the Germanic forms, such as simple verb and adverb/preposition combinations.

For example, we also say 'go out' or 'come out' rather than 'exit'. We say 'come down' and 'go down' rather than 'descend', and 'come up' and 'go up' rather than 'ascend'. We reserve the Latin words for formal, academic, technical, legal, scientific and literary contexts.

As Michael K says, 'enter', as a Latin word, sounds very formal and cold. It's also less meaningful/

'Come in' is  more informative than simply 'enter' because it contains two elements - not only the instruction to enter a room, but also the instruction to come towards the speaker. Compared with French, the Germanic/English forms are more flexible - 'entrer' can be expressed as either 'come in' or 'go in', depending on whether the person is going towards or away from the speaker, and 'sortir' can be either 'go out' or 'come out' depending on the relative direction.

As Michael said: "come in" sounds welcoming. That's the nature of phrasal verbs.

"Enter" sounds like a command. That's how the words borrowed from French/Latin sound to us: authoritative and cold.  I think the confusion here is that you <em>are</em> translating directly, and not thinking about it from an English perspective. :)

A propos.. yes, it's French, but we use it in English too when we want to sound elegant.. à propos of the Latin/ Germanic roots of the English language, here's another example which is often cited:

In the centuries following the Norman invasion of 1066, there were two languages spoken in England : ordinary people spoke Anglo-Saxon, while the ruling classes spoke French. The peasants gave Anglo-Saxon names to the animals they looked after, while the lords and ladies in their castles used French words for the meat that was served to them. The peasants rarely ate meat, while the ruling classes rarely thought about the animals in the fields.

This social and linguistic split still has its influence on the language of today. For living animals, for example, modern English has the words cow, sheep and swine (pig) , which are very similar to the modern German words 'Kuh' 'Schaf' and 'Schwein'. Meanwhile, the French influence is obvious in the corresponding names for the meat of these three animals : beef, mutton and pork (boeuf, mouton and porc in modern-day French). A thousand years have passed, but the linguistic legacy remains.

Because "come in" sounds more welcoming. You can say "enter" but it sounds really formal and cold.

Hard/difficult - Same meaning, but "hard" sounds more casual.

Town/city - They mean different things. A city is bigger than a town, which is usually smaller and in the countryside.

Answer/respond - "Answer" is more casual.

House/mansion - A house is just a building where someone lives. A mansion as a large, multi-million dollar house where rich people live.

Smart/intelligent - "Smart" sounds more casual.

Wealthy/rich - "Rich" sounds more casual.

Student/pupil - "Student" sounds more casual.

Teacher/professor - These are different things. A teacher is anyone who teaches. A professor teaches and runs a course at a university. They're technically teachers, but they could get offended if you call them that!

To forgive/to pardon - "To forgive" sounds more casual. "To pardon" is usually only used in legal settings. 

Old/ancient - "Ancient" is older than "old". I was taught in school that "ancient" only refers to something that existed before the collapse of the Roman Empire (regardless of whether the object belonged to a different culture or not), but you can just think of "ancient" as meaning "very, very old".

Weird/strange - "Wierd" sounds more casual.

Big/huge/large - "Big" is more casual than "large". "Huge" is bigger than "big/large", but smaller than "enormous/gigantic".

Pretty/beautiful - These are used slightly differently. When talking about women, "pretty" is more likely to be used to refer to young girls whereas "beautiful" is more likely to refer to (relatively) older women. "Pretty" usually isn't used to refer anything that's not human, but you could use "beautiful" to describe any kind of view or work of art.