Both of those should be looked upon with suspicion. I can't say "never do it", given that every employer I've ever worked at has had its own proprietary database, and one of the projects I worked on at Google was a proprietary template language. But all of them were a large maintenance burden, much larger than originally anticipated.
I think the old business adage about "In-source your core competencies, outsource everything else" applies here. If you derive a big competitive advantage from having a proprietary database or proprietary template, and it generates enough revenue to afford a dedicated team of experts to maintain it, build it. But if you have a bunch of smart & motivated developers who can build a proprietary database, but your product isn't databases or templates and your core differentiator isn't the performance or query patterns you get from building it yourself? Put them to work improving the product, and work with the infrastructure that other firms have built already.
I think the old business adage about "In-source your core competencies, outsource everything else" applies here. If you derive a big competitive advantage from having a proprietary database or proprietary template, and it generates enough revenue to afford a dedicated team of experts to maintain it, build it. But if you have a bunch of smart & motivated developers who can build a proprietary database, but your product isn't databases or templates and your core differentiator isn't the performance or query patterns you get from building it yourself? Put them to work improving the product, and work with the infrastructure that other firms have built already.