Quick googling located online version of Lodish et al Molecular Cell Biology. 4th edition.
From TATA Box, Initiators, and CpG Islands Function as Promoters in Eukaryotic DNA section:
These genes, which generally are transcribed at low rates (e.g., genes encoding the enzymes of intermediary metabolism, often called “housekeeping genes”), do not contain a TATA box or an initiator
Also, from Transcriptional Regulatory Sequences of the Housekeeping Gene for Human Triosephosphate Isomerase (Boyer et al, J Bio Chem 1989):
In contrast to facultative gene promoters, these promoters are
characterized by [...] and, notably,
the lack of an appropriately positioned TATA box
Based upon these structural differences,
the possibility exists that initiation of housekeeping and
facultative gene transcription proceeds through distinct mechanisms.
I can imagine you can google more information, but it seems to me that reason for lack of TATA is necessity for constant low-level expression (hence no strong promoter) and separate mechanism of regulation (hence some common structure). Last point might arise from redundancy argument: when regulation of TATA-containing genes become faulty, housekeeping genes regulation stays same because it is somewhat independent.
However, you should be aware that your original assumption is at least controversial (from same J Bio Chem paper):
Unlike most housekeeping gene promoters that have been
described to date, the human TPI promoter harbors a canonical
TATA element (5’ TATATAA 3’) that spans positions
-27 to -21. LS mutagenesis demonstrated that this TATA
box clearly represents a control element, the integrity of which
is essential for the maintenance of both the fidelity and the
frequency of TPI gene transcription initiation.