1. Coming from a client-side rendering perspective, DOM morphing/diffing is 99% of the time a bad idea, except in the case of reordering a list of keyed items where you can use a simpler, more specialized algorithm.
It's much better to use template identity to compare the source template of the current DOM with the source template of the incoming DOM (or description of DOM) and completely re-render if the source template changed. It's a very simple and fast check, and nearly all the time you change templates you want new DOM state anyway.
This technique works with SSR'ed HTML as well. You leave marker comments in the HTML that bracket the nodes created from a template and carry with them a template ID (e.g. a hash of the template). When updating the DOM, as you traverse the template instance tree, you check IDs and replace or update in-place as needed. Again, simple and fast.
2. But... If you're morphing the existing DOM, this seems to eliminate many of the benefits of sending HTML in your server responses in the first place. The HTML is just data at that point - you parse it only to crawl it as a set of instructions for updating the DOM.
HTML is an expensive way to do this. It's a larger format and slower to parse than JSON, and then you have to do this diffing. You'd be better off doing client-side rendering if possible. Data + templates is usually a very compressed format compared to the already expanded HTML you get from rendering the templates client-side.
And if the reason to morph is to keep things like event listeners, templates would let you attach those to the new DOM as well as preserve them in the unchanged DOM. With DOM morphing you need a way to go set things up on the new DOM anyway.
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The big advantage of this is the architectural simplicity of only ever returning HTML from the server, as opposed to HTML for first render and data for updates, but it's not going to have good network and rendering perf compared to CSR for updates.