Personally, I often set up a challenge where the outcome is dependent on Asset cards played. So an example, in a group fight that needs 9 cards to be played I note that at least 3 weapons are needed to qualify for a strong outcome. So, even if they finish "strong" but don't use 3 Asset cards, I treat the outcome as a weak one.

An alternative to this is to simply add on, much like the number of cards needed for a challenge, additional "Asset/Goal" boxes. As it is now, I hardly ever see people playing their goal cards or items from their inventory. It's almost easier to think of a weakness or strength in relation to the goal.

At the moment there are very few occasions when it makes mechanical sense to play an asset. (I know there are usually plenty of fictional/ narrative reasons) - but viewed from a purely mechanical/rules sense it doesn't add up.

Strengths, Weaknesses and Wilds balance towards uncertainty (ie equal numbers of strong and weak) but are worth playing because they lead to refresh and a chance for character development.

Subplots are worth playing (especially if the pool is small) due to the reward.

Assets however push towards uncertainty and offer no reward. There are in fact only two occasions when mechanically they are worth playing:
1) When you want to play two or more cards on a challenge but don't have that many Strengths, Weaknesses, Wilds or subplots
2) When you want the strong or weak outcome on a challenge but your other cards wont allow you to achieve this.

Can I suggest the following tweak to the suggestion though

Rather than unlimited use (which could be unbalancing), set a 3 cards plus one asset limit. i.e you can exceed the three card limit by a single card so long as one or more of those cards is an asset.

Then it is well worth playing assets.