Scholar Sultan Barakat points out that in the first six months after the outbreak of war, Iran seemed to be trying to avoid the Red Sea becoming another major front. Keeping Saudi Arabia and Egypt, two key Arab states bordering the Red Sea, outside the US-led military bloc was clearly in Iran's interest. It's reasonable to speculate that Tehran initially asked the Houthis not to provoke Saudi Arabia. However, Saudi Arabia's July attack on Sana'a International Airport changed this calculation. Iran may not want to see Saudi Arabia confront the Houthis, but once the Houthis decide to respond, Tehran can hardly expect them to remain passive, otherwise it would undermine the credibility of the alliance that Iran has previously maintained. Escalation also serves Iran's interests, but it doesn't mean Iran ordered the Houthi offensive.
Given soaring fuel prices and inflation in the US, the Trump administration is likely closely monitoring the escalation in Yemen, but this may also present an unexpected benefit for the US. Until now, the US has struggled to persuade regional and international allies to join its confrontation with Iran. Saudi Arabia and Egypt have always had good reasons to distance themselves from the US, but the direct threat to the Red Sea will change that. Even without formal cooperation, US coordination could align Israeli, Saudi, Egyptian, and European forces in a naval confrontation. Therefore, the Houthis could potentially achieve the opposite of Iran's initial intentions. By threatening the Bab el-Mandeb Strait, they could encourage Saudi Arabia and Egypt to gravitate further towards Washington, while simultaneously forging a new, largely unrecognized coordination mechanism with Israel.