This is a good point, I do wonder why China aren't getting involved. Some 60% of their trade with the EU
goes through the Suez canal, you'd have thought that was enough incentive to act. Maybe they realise that an ineffective bombing run against Ansar Allah is going to do nothing for their military reputation.
Possibly the thinking goes:
1. China -> Iran -> Yemen means china controls shipping trade lane of India, and any Asian country.
2. China won't say or do anything to US/UK/EU defence because military action pushes local countries towards China in defence - they'll buy Iranian weapons for the low prices but Chinese weapons of they can afford it now USA is less likely to allow modern weapons to be sold (f16 maybe)..
3. Yemen and other countries aren't really boundaries - they're tribal in their allegencies, so they will operate until nullified and other will step up. The impact is likely to be small.
I suspect that US/UK etc are concerned that missiles are one thing - Iran/Russia will sell mines and the Yemeni Houthi will make the step of mining international shipping lanes - I think China would prevent this due to the long term economic impact. It's also not clear what would happen if those mines ended up drifting out of that zone - local tensions would also impact. However they don't care because they're not thinking economy but ideology.