First, an assumption: given what I know about tip-sleeve and tip-ring-sleeve connections, using a TRS cable between two TS jacks just yields an unused contact/conductor in the cable.
Other than cost, all else being equal, is there any reason I should buy and use TS cables instead of TRS cables for various connections in my small studio?
One "typically TS application" that would definitely present an issue is the connection between a guitar with active electronics and an effects unit (stompbox).
The output of the guitar and the input of the stompbox almost always have a TRS jack that is used to power the device on:
One battery terminal (usually negative) is connected to the Ring terminal of the jack so that when a TS cable is inserted, it shorts the Ring and Sleeve terminals to connect the battery to the ground in the electronics.
Putting a TRS cable between two such devices connects their batteries together through the "floating" Ring conductor, with unpredictable results (and possible damage).
Using a TRS from an active guitar to a "universal" input (like on some audio interfaces) designed for either unbalanced TS or unbalanced TRS may apply battery power to the interface unit. It's probably blocked by a capacitor so as not to cause damage, but this is not guaranteed. The guitar electronics are not likely to power on.
Using a TRS cable between an active guitar to an amplifier or between a passive guitar and a stompbox may work, but is not guaranteed.
No, for a small studio, other than the cost difference, you can use TRS in the place of TS cables.
When you start looking at cable runs over around six meters (20 feet) you can start seeing some issues with resistance, depending on what you are using the wire for. The dual wire TRS cable will sometimes have a smaller gauge wire than the coaxial cable that is often used for TS.
Usually there is no significant difference though.
EDIT: thinking about it, there may be some slight durability difference in the two types of cables as well, if you are using the TRS cables in applications where they get flexed often, such as for a guitar cable. The tensile strength of the single wire is likely higher, resulting in a longer life before breakage in high flex use.
I wouldn't use a TRS cable in a TS socket because it's a tossup whether or not R makes contact or not. So you have a connection that will willy-nilly add a twisted core redundant core in parallel to the shield and not. This is quite unlikely not to result in handling noise.
In addition, a TS cable is coaxial and usually intended for high-gain high-impedance connections. A TRS cable (the twisted-pair variant for balanced connections, not a stereo cable) is not coaxial and intended for low-gain low-impedance connections. Not being coaxial means that it has quite higher parasitic capacities and inductivities than a straight coaxial cable which has a fixed geometry and dielectric between shield and core. This is important for high-impedance connections.
In contrast, a TS cable in a TRS socket is well-defined behavior and is often used for audio equipment that may accept balanced or unbalanced connections.
TRS cable may not work with active guitars, sometimes the additional pin causes short circuit.
Cutting all the nonsense - use TS for mono and TRS for balanced and appropriate cables - why? Because you don't know what the female socket on mono will touch - in ideal world, yes it should touch ground but in practice I had few cases that it was getting second leg of balanced signal (interface to amp as example). If you can't afford proper cables then I would say, try TRS and then TS - in 80%-90% cases it should be ok, if there is difference in signal use proper one.
