It seems to me that a constant mashgiach would still be required.
For background, there are 4 main problems with a vegan restaurant without any mashgiach, as summarized from ok.org, and chabad.org:
- Vegetables can often have insects. The Vegan Society allows for a minute quantity of animal products to be included in food advertised as 'vegan'. That does not, however, make the food kosher.
- A second issue is the restaurant equipment. Many restaurants use pre-owned utensils. It is not possible to know if the equipment was only used for kosher food (also unlikely). Although there is a heter if the vessels were not used for 24 hours (ein ben yomo), that is only permissible b'dieved. But even with that, employees will often use restaurant equipment to prepare their own food. Therefore, even ein ben yomo will not help.
- A 3rd problem is that the food itself is likely to be bishul akum. Bishul akum is permitted by a) food that is edible raw, and b) food that is not fit to be served by a king's table. Granted, most food will fall into either one of these categories, but other foods, like fancy potatoes, or grains and rice, will be prohibited because of bishul akum.
- Wines and grape juice need a valid hechsher. The restaurant may not have a wine list, but these beverages may be used as ingredients for some dishes. (I haven't found a source for this, but it is also possible that if they wine is not mevushal, there is also the problem of yayin neshech.)
Regarding factories only requiring surprise mashgichim, that is the exception, not the rule. A sporadic mashgiach only helps if we're afraid of intentional cheating in a long term scheme, in a case where if the mashgiach shows up unexpected he is very likely to catch them in the act. However, in the case of the vegan restaurant, (as you yourself said) we are not worried about intentional cheating, as the prices are similar (also R' Moshe's heter of uman lo mera umnutei-they won't risk their business by buying nonkosher ingredients). Because we are afraid of innocent, unintentional mistakes which may happen at any time, the restaurant will need a constant mashgiach. (For more info, see Torah Musings)