They didn’t say potatoes are unhealthy they made the valid point that eating nothing but potatoes might be. As well as unnecessary, there’s a whole world of vegetables this guy could choose to discover and eat and still lose weight.
To expand on this, vegan diet is more demanding with regards to planning than meat-based diet as there is no single vegetable that contains nutrients that people need and even then you still need to balance your macro (ie. proportion of carbs to proteins to fats).
Meat is an easy choice as it roughly contains what you need in roughly right proportions. It is not the best solution to the problem (I don't want to say eating meat exclusively is healthy or better than vegan) but it puts you in roughly safe spot in that you can be extremely lazy with the diet.
With vegan diet you can quickly cause a lot of damage to your body if you are not paying attention to what you eat.
If you don't want to spend your days with calculators and tables the safest bet is to just vary everything -- eat a little bit of everything every day or different things every day.
One tip I would give even if you don't want to pay a lot of attention to details is to still try to manage proteins / carbohydrates / fat content of your food. Just add olive oil when you don't see enough fat in your food, etc.
