Vulkan supporting Unreal Engine 4 has input latency issues that generally makes in unusable for a large proportion of games without some issues. This leads most devs who are worried about input latency to find a different engine. Unity is the only other publicly available engine, accessible to everyone from indie to triple A (Though there is good reason why it’s not used in triple A games) that has Vulkan support. The issue is that Unity relies on C# and other interpreted scripting languages for the game code that negates any performance improvement you might see by using Vulkan.
This leaves devs with three options. Don’t use Vulkan, Adopt an engine where the source code is available to be modified and then build Vulkan support into it, or build up a new engine that supports Vulkan.
Generally, Large studio’s use in house engines. Whether it’s an engine built by themselves or another studio under the same publisher.
medium studio’s depend on the type of game. Some build their own engines, other’s use existing ones. Small studios generally use existing engines. Tiny indie teams (1-3 people) are again a mixture. Some use existing engines, others build their own.
Building an engine isn’t actually that hard when used for a specific genre. It’s accessible to any dev team with an experienced developer. The issue comes where you need to build tools and product pipelines to make building the game accessible to designers.