If they keep the same place, now you have to manage not only the content but also the order. If they shift around according to some metric like 'most used' then you have to visually search for the correct tile.
And this is assuming that the collection is small. Otherwise paging or some other kind of grouping has to be used which is horrible.
Tiles aren't even that easy to use. They always require visually processing and then coordinating the action. With typing it's just muscle memory.
They also require some kind of image which adds another dimension the problem. Now those tiles have to look good, or be colored according to some kind of logic. This styling can also impact usability, e.g. getting the icon/logo of the site can look ugly.
Tiles make sense in a touch context environment like mobile or tablets where typing can be cumbersome. But in a desktop environment it would be a lot worse.
We have thought about maybe having your top 3 most-used Zapmarks appear under the search bar for quick access, but not sure if that's something we will move forward with or not. ¯\_(ツ)_/¯
Anyways not raining on you’re parade. It’s a cool concept just doesn’t fit the use case I’d prefer. Best of luck with it!