When I was a young man I really, really wanted to buy a new sports car. But being in the army and, later, graduate school, my income made that a marginal proposition. As a grad student with teaching assistant and summer research pay, I could (barely) afford a later version of the Sprite. I rejected getting one because I thought it was too small from a safety standpoint, not to mention its limited capacity for carrying things such as suitcases or even groceries.
As for the first-generation Sprites, the bug-eye feature was an additional turn-off. They made the car look cheap.
From various sources including the above link, it was originally intended that the Sprite's headlights would be hidden when not in use. They would pivot upwards when turned on in the manner of cars such as the Porsche 914. However, this feature was rejected for reasons of cost. Another solution would have been to place headlights on the front fenders, and this was done on the second-series Sprites.
In summary, the Sprite was designed under extreme cost restrictions, its shape greatly influenced by engineering and production considerations. The Wikipedia names two designers who had to work under these circumstances, so it seems that the Sprite was not a total product of engineers.
Like a number of cars considered odd in their day, surviving Sprites have affectionate owners and fan clubs.
