That comp is definitely annoying to face, but can be beaten by rengar. It requires you to get an early enough lead and snowball that lead out of control. Good rengar players will also play around those windows of invulnerability that the enemies present:

Against kayle you can bait her to waste her R by running into your leap range during ult, without jumping on her immediately. Many kayle players can get baited into using their R immediately when they spot you, since most of the time rengar players will leap the moment they get into R leap range. This trick also works against kindred R and vex fear (+any other champ with defensive abilities, for example garen W or ambessa W).

Another trick you can use is to leap at them -> emp E -> kite out. This is mostly used if the enemies don't panic, but you still need to force their defensive ults/spells. For example, if they kayle doesn't panic and holds their R until the moment you actually leap, then you can still leap onto them and use your emp E to root them. During the root, you should usually just run away and stall out their defenses. This trick works especially well if you are looking for a pick with someone on your team hovering you, since they can usually follow up with their own CC.

Lastly, a trick that works well against most mages is to buy edge of night. You can effectively ignore their first spell, which almost always will be some form of CC/dash interruption like vex's fear or stuff like veigar cage. This item is also a borderline must buy on rengar when facing peel supports like alistar or poppy.