First, most of the time for similar spells you don't get to choose the creature's type. Only conjure elemental specifically says that you choose what springs forth. Most of the time, you just get a choice of what CR you want the creature to be. While some/most groups will allow the caster to choose which type of creature they summon, ultimately the choice lies with the DM. Primarily this is to prevent powergaming of always choosing the best monster. So specifically allowing for you to choose what kind of undead shows up breaks convention.
Second, other similar spells like conjure elementals has the line "The DM has the creature's statistics" at the end. It seems like this is to prevent players to have access to the statblocks of fire elementals and the like. In those few cases where the player does have a choice of what to conjure, like in animate dead, there are actual statblocks the players can see, in the Appendices. So this spell not having that line brings up two problems: first, the players will be wanting access to the MoM to be able to pick and choose what creature they want to summon, when they should be content with the HHB like how normal players use the PHB. Second, since spells that do allow choice usually come with a statblock in the appendix, as choices increase via the various expansions, the HHB will have to be expanded along with them. (Or not, but that doesn't feel right to me.)
Tasha's guide also has a spell named Summon Undead. To avoid confusion, our version should be renamed to Conjure Undead.