David MacKay discusses this in Sustainable Energy Without the Hot Air. He concludes that, while it's on first glance appealing to want to use waste heat from power generation, heat pumps are strictly superior to combined heat and power except for in a few specialized circumstances (e.g. industrial uses that require high temperatures). The book is fifteen years old now, so I suspect the math even more strongly favors heat pumps than when it was published.
See the section, "Heat pumps, compared with combined heat and power": https://www.withouthotair.com/c21/page_147.shtml