When you purchase the DXP platform you get Search & Navigation (Find) as part of it which uses Elasticsearch with a far better .NET wrapper and far better admin/editor management feature set. Lucene also can be tricky with scaling instances due to the way it writes the lucene data so S&N/Elasticsearch is far better option.
With search and navigation you get boost, set synnoynms, related queries and auto complete all out of the box. It also has tracking and if using commerce support direct built in personalization for commerce searching.
@postjoe, I think the reason why it is not supported is due to the fact that Lucence is a filebased search solution. Taking this into account you can then see why this is not a good option when working with the cloud. The lucence index would need to be stored upon the web app, which is not a good practice when working with cloud solutions.
Scott and David have already mentioned that DXP comes with 'Search and Navigation' which has many benefits. Having worked with Lucence in the past and now mostly focused on search and navigation I would never go back. The ease of using find is one of the selling points for using the product. You will not loose functionality by switching from Lucence to search and navigation and will instead gain more control over your ability to perform searching.
To give you a better answer as to 'why'? We would need more information around 'why not' switch to Search and Navigation?
Technically? Not really. But as many mentioned, DXP subscription bundled with Find (Search and Navigation) which is simply superior, and you can migrate very easy to. We of course want to upsell our products and provide the best experiences/services to our customers, so there is no point of bringing Search to DXP.
DXP, I am told, does not support Lucene for search, I am looking for more details on the "why". I am looking for technical/developer documentation.