English can be read in a different order than the normal order when the sentences contain words for which it is easy to guess whether they are agents or patients, e.g. when the agents are animate nouns and the patients are inanimate nouns, or when pronouns are used for the agents or patients.
Otherwise, the non-standard order can be understood incorrectly. While the distinction between agents and patients is the most important that depends on word order in English, there are also other order-dependent distinctions, e.g. between beneficiary and patient, when the beneficiary is not marked by a preposition, or between a noun and its attribute, e.g. "police dog" is not the same as "dog police" and unless there is a detailed context you cannot know what is meant when the word order is wrong.
English is one of the languages with the most rigid word order. There are languages, especially among older languages, where almost any word order can be used without causing ambiguities, because all the possible roles of the words are marked by prepositions, postpositions or affixes (or sometimes by accentuation shifts).