As Lee Dembart says above, there is a difference between a phrasal verb (as a unit) and a verb followed by a preposition. Your poll will likely result in 100% agreement with "I walked into a lamp post" because there is no debate: the verb is "walked" (not "walked in"), and it can be followed by different prepositions (e.g., I walked around the lamp post). Canadian Oxford Dictionary states that "walk in" is often followed by "on" (e.g., "I walked in on them," which contains a phrasal verb followed by a preposition).
A better example might be the phrasal verb "hold on," which is different from the verb "hold." Copy editors would not close up "on to" in "They hold on to family traditions" or "He managed to hold on to his property." But "Hold on to/onto your hats" would generate debate, no doubt.
There's a phrasal verb, "to walk in," which is intransitive and which means "to enter." (The meeting had already started when I walked in.) If your construction uses that verb, and you want to emphasize the idea of entering a room or a building or whatever, it's possible to keep the "in" separate from a "to" that follows it. If spoken, there would be a slight, barely noticeable pause between the two words. (I walked in to the meeting.) Or they could be closed up as one word. (I walked into the meeting.)
In the case of the drawing, however, there's no idea of entering anything. It's a collision, and the two words are written and spoken as one. You walk into something. You don't walk in to it.
By the way, my dictionary, the American Heritage Dictionary of the English Language, 4th edition, has "lamppost" as one word.