Ever wonder why you ever need to spend so much resources putting up the different Amenities to unlock further friendship levels with animals? Well, the main reason for this is that the higher your friendship level with animals go, the bigger chunk or portions of rewards they hand out to you every time you successfully manage to fulfill their requests.
For instance, if they might have given you 1 or 2 pieces of Cotton every time a request is fulfilled at lower friendship levels, fulfilling a similar request with a level 10 friendship (with the same animal) would instead make this around 5 pieces cotton. Not limited to this example, every time a further friendship level is reached (with a specific animal), you should immediately see an increment in their rewards.
More so, there are instances where animals would start to reward you with better/unique items upon reaching a specific friendship level with them. In return, these items would (if not outright) open up/unlock new possibilities in the game in the form of new items that are plausible to Craft. Often times, animals would request for something unusual or something that is relatively different from what it usually asks at levels 10 and 15. In return, fulfilling these requests usually awards you with unique items to craft (with the rewarded item/material).
Lastly, when you reach the maximum cap level for each animal (level 20), that specific animal will give you his/her portrait. In essence, unlocking content in the game heavily lies in reaching each of the maximum friendship levels with the different animals in the game. Given that, purchasing the different Amenities in the game is the only way you can increase each of these animals' maximum friendship levels.