No, we don’t recommend it! It’s wasted money (74 euros?) if your country is eligible for a 3 months visitors’ visa.
If I don’t take the student visa, do I need to buy a ticket proving that I will leave Taiwan?
Yes! We know several students who were refused from boarding the plane because they didn’t have a formal proof that they would leave the country within 3 months.
The solution? Buy a cheap ticket to Hong Kong, the Philippines, Japan or South Korea to go on holiday during the school vacations. You’ll have 3 months in Taipei to make friends and to convince them to travel with you. It’s easy! Don’t throw away those 74 beers (did I mean euros? 
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Note: Plenty of expats use this trick here. Universities will not recommend it because it’s in their interest to cover themselves in case someone doesn’t read the info thoroughly. As public institutions, they will always recommend the safest solution.