VImagine you got 100V pulse at your V1 + pin but not versus V1 - pin but versus GND.
Nothing will prevent this pulse from going to your load.
So we are mainly using the TVS for ESD protection such as lightning, IEC compliance. and assuming that the TVS diode can handle the transient,
Just think about my 100V example. Your TVS will not notice it at all and this 100 will go to your load (I am ignoring at this moment a problem what diodes are - assume they are 1000V).
Don't mix all the time ESD with lighting as we don't know against what you are trying to protect your circuit.
ESD is from your finger - is very fast (nanoseconds), can be even 25kV (3kV ESD from your finger you even not notice, but device can be damaged).
If ESD from your finger be put into your V1 pin it will be searching a way to GND and not to second V1 pin so it will ignore your TVS. Your TVS protects V1 against being forced to higher voltage between its + and - pins but not protects your load.
When we speak about lighting effects we speak about surge pulse. It is much slower (microseconds) and longer (so much higher energy). As you are probably not building energy supply for building you need not assume direct lighting but only indirect effects mainly by lighting currents traveling through GND. In such case it strongly depends on where are located your two devices (V1 source and load). The situation is much different if they are located in separate buildings then if they are both in the same building (with common grounding system).
ESD protecting diodes must be very fast and with low ESL (equivalent series inductance) because very high dI/dt of pulse can produce high voltage at ESL. I remember reading (20+ years ago) of someone who measured 200V pulses generated by ESD at low voltage Surge diode (it was possible because its high ESL). But ESD protecting diodes need to withstand smaller energy that surge protecting diodes. Surge protecting diodes are bigger but you don't worry of having because of it higher ESL as these pulses have much smaller dI/dt.
Except ESD and Surge you should also consider Burst pulses, but as they are 'between' these two if you protect against ESD and Surge you in most cases are also protected against burst.
TVS diodes do not protect devices alone. They 'cooperate' with serial impedance (it can be cable impedance or intentionally inserted serial element).
EMC standards regarding your device specify against what pulses levels you should protect its pins.