Why are multiple 学s okay in the sentence 我学英语学了4年了
The interesting phenomenon in this example is the use of 了。。。了 to indicate an ongoing action. In cases where the ongoing verb takes an object (like 英语 in your sentence), the verb is repeated. If the object is understood, it doesn't need to be repeated. For example, if you've established with your interlocutor that you're studying English, you might say 我学了一年了 (I have studied for a year).

As an aside, your "naive translation" would be closer to "I studied (i.e., completed studying) English ...". If this is your intent, a more apt translation might be 我学了四年英语