I think it is important to make the disctinction between level setting calibration and setting the bias.
Those tasks are usually lumped into the activity of "calibrating", but they are different.
Setting the bias is the process of adjusting the output of the bias amps (which present a very high frequency tone to the tape, usually between 100kHz and 150kHz). The high frequency bias signal, which is present at the erase head, "excites" the oxide preparing it to receive program material at the record head. The ultimate goal is to have the bias level adjusted so that recorded material has the minimum amount of distortion. I won't get into special effects biasing which is over or under biasing on purpose to elecit particular character out of specific source material. Bias requirement does differ between tape types and brands, even "bias equivalent" types ("Quampex" 456 and BASF/EMTEC/RMGI SM911 for instance). Bias requirement could even be slightly different between different runs of the same make and type of tape. Can you hear the difference if you don't rebias? I don't know...let your ears judge. You're not going to break anything, but to suggest that you can swap tape types and brands and the bias will be in the ballpark is a bit of a stretch AFAIC.
Calibrating levels is different. That is setting the machine up so that "0" on the VU meters (when monitoring the input and reproduce signals) represents some level of signal (of your choosing) and that all tracks are consistent with each other. The sky is the limit when it comes to what "0" means compared to what type of tape you are using and what kind of material you are recording.
If your machine is setup as is typical for a "+6" tape where "0" represents 250nWb/m, and you put a +3 tape on the machine then you will reach saturation earlier with the same amount of signal as compared to using the +6 tape. That's just a simple example. Go the other way and put a +9 tape on without recalibrating and if you setup your input levels the same way (keeping "0" as "0" and your recorded signal will be less saturated and you will likely have more tape noise since you won't be taking advantage of the headroom afforded by the +9 tape. Keep in mind also that not all record/reproduce amplifer sections are happy with pushing the level of signal required to saturate +9 tape. No matter. Use +3 tape and soak it with signal. Some seem to think that a higher ouput tape means more "phat tape compression" but what it REALLY means is that you have to run all your signal hotter to saturate the tape...I see higher output tape as being more for quieter operation particularly if you don't use noise reduction than "phat tape sat". You want tape saturation? Then set your deck for "0" at 250nWb/m or even 320nWb/m and use +3 tape. You'll reach saturation sooner without taxing your record/reproduce amps.
The balance of the calibrated operating level of the machine and the type of tape is one of the beauties of using an analog tape machine...balancing saturation and noise level of the setup with the character of the tape type.
Try out different settings or tapes and see what you think...the subjective can be quantified by the objective setting of the machine and the tape type and that can be useful info.