My understanding is that cold starts on containerized Lambdas is actually better than non-containerized for some workloads, because using containers allows Lambda to do better caching of the code, as well as lazy-loading. YMMV of course based on exactly what image you use (eg if you're not using a common base, like Ubuntu or Amazon Linux, you won't get as much benefit from the caching) and how much custom code you have (like hundreds of MBs worth).

There's a very interesting blog post about it here, as well an an accompanying whitepaper: https://brooker.co.za/blog/2023/05/23/snapshot-loading.html