Pre: My views may be clashing with some people. I express as far as I know.
To start with, hybridization is a hypothetical concept$^{1}$ just to explain all facts and make our work easier, otherwise we would have to take into account every single interaction of electron-proton and also other phenomenons; many theories developed which explained all the major/important facts at a macro-level. And what I have been saying to take into account was all micro-level analysis. 764
Attributing hybridization is purely personal choice because neither does it account all facts(for some molecules) nor it can be dropped altogether( for its $\cdots$ ) ,if then we would look for another theory$^{2}$ to explain observed phenomenon.Parallels similarity between this and the situation of Ideal-Gas equation, in general no perfect theory has been developed, but the most easy, practical and useful are the hybridization$^{3}$ and vander-walls equation*.
As we move downwards in the periodic table the hybridization concept fails at many places due to overpowering of other factors.I wonder you didn't mentioned the bond angle$^{*4}$ ($93.5^o$) for a $sp^3$ hybridized (ideally $109.5^0$).
In general atom/molecule doesn't seek to follow a theory, it does what it is best comfortable with, it is us, who mould the theory to the observations.
As a genral rule, for sake of convinience, assume all molecules show hybridisation and the tendency to hybridise decreases down the group.
In conclusion, I would say it depends on the need of the situation and such dubious statements such as "Does $PH_3$ exhibit $sp^3$ hybridization?" should be replaced with "Does hybridization explain all(actually not all) properties of $PH_3$"
Also there are weights in $sp^\alpha$ where $\alpha$ ranges from 1 to 3(even upto 4$^{*5}$ and maybe beyond) and is in between these for $PH_3$ and some may continue to treat it has a hybridised molecule with suitable weights.
$^{*1}$(as far as I know)
$^{*2}$(probably the MOT)
$^{*3}$(many may argue for other theories which is genuine, but in context this follows)
$^{*4}$(One may argue as we move down the group electronegativity decreases and atomic size increases. In case of $NH_3$ due to higher bond pair bond pair repulsion ( since electronegativity of N atom is very high hence it attracts bonded electrons of N-H bond towards itself) bond pair moves away from each other and hence shows greater bond angle. This may be considered one of the major factors for less hybridization.)
$^{*5}$[$O$ in $H_2O$ which means that they have 20% s character and 80% p character, but does not imply that they are formed from one s and four p orbitals] 979