If it makes you feel able to work with the mails more efficiently and if your volumes are such that you were still seeing performance issues, then that’s a couple of good reasons to filter down your mails.
Deletion is certainly a good thing to do and will help get your volumes down. If you are ruthless, then this can be a very quick way to reduce volumes.
But, I suspect you will still have a lot of mails to search through which it sounds like you may still find overwhelming.
I would still suggest that it would be worth prioritising the mails you actively work with and search for. Filtering for those and moving them into a suitable folder structure should both reduce your “old mixed mail bucket” volume while making the mails you are going to be active with more accessible for you. i.e. tackling in the opposite direction might give you better returns sooner; but both approaches effectively costs over at some mid-point,
There is a threshold of course. If you can quickly reduce volumes to a point where an “archive search” is acceptable, that could actually be a better approach, but this would still lead to you having to deal with unwelcome larger volumes over time. But this initial deletion would then make it quicker to search for active sets of mails as the overall volume would have reduced significantly.
So, if you want the organisational benefit asap, I think prioritise and file is still your best option at this point. If you are okay to continue searching for a while, and the smaller active folder approach is fine as a longer term goal, then I would continue with your current approach.
One final thing to highlight is that if you are just highlighting mails and hitting the delete key, then this is a tactical solution for here and now. If you want to apply it more strategically, consider using rules to tackle as many as possible as they can apply on an ongoing basis and save you work in the future. After all automation is the name of the game