There is another point to remember here. This was supposed to be a two-parter campaign - Dragon Heist followed up by Undermountain. How much time do you want to spend on levels 1-5? Do you want this to be a major element of the campaign, or, more or less, the prelude leading up to the main course of Dungeons of the Mad Mage? Dragon Heist is only supposed to go from levels 1-5 - basically grounding the group in Waterdeep, probably introducing some of the movers and shakers of the setting, and serving as a starting point for delving into DotMM.
From that perspective, expanding out Dragon Heist probably isn't that necessary. Levels 1-5 are pretty quick, and, other than tying the players into the setting, there really isn't a whole lot else needed here. Having the different factions play a bigger role in DotMM, with the different factions all pursuing different and often conflicting goals means that the PC's can continue to be engaged in the Waterdeep end of things while still doing DotMM.
Or, conversely, you can certainly turn Dragon Heist into an entire campaign on its own, but, that's going to take a LOT more work.