I think you are picking up on several features here, which I will attempt to disentangle.
The first is the allocation of tone numbers in IPA versus "reality". Tone "letters" were proposed in the IPA by the most illustrious linguist in Chinese in the 20th century, Yuen Ren Chao, in 1930. The numbers were assigned later. One can see that it's particularly adapted for the multiple-(pitch) register contour tones of the Chinese varieties. In general, it fits into the schema (I hesitate to call it a theory) of High, Mid, Low that is intuitive to most people. The key here is relative tones.
However, what is the difference in actual frequency between 3 and 5, or 1 and 5? Everyone is different, and it is true that studies can vary (sometimes wildly). E.g. the studies of the Eastern Min dialect of Fuqing vary in their description of their tones (whether there are that many falling tones or whether some of them are level pitch).
Mandarin Chinese has had its standard version reinforced through pedagogy for the best of 50 years (and perhaps longer) now, and so the 55 vs 35 vs 214 vs 53 has been trotted out so much to become a paradigm for a contour tone language in general. Does this really represent how actual Mandarin speakers speak now?
That brings us onto the second issue, documenting variation. There have actually been studies on this between Beijing and Taiwan Mandarin. Most natives as well as learners (on both sides of the strait) will characterise Beijing Mandarin as having a much higher and wider pitch range, with Taiwan Mandarin much less. This is borne out by the research (figure 4.6 is particularly wonderful, although it doesn't show contour). We can see fairly clearly nonetheless that there is a variation in absolute frequency. However, is relative frequency affected? I'd say that only tone three (historically 上聲 / 上声) is actually different to 213 (should be 21 in Taiwan, all the time).
This brings us to another aspect of variation: variation of context. It is well documented that Mandarin tone three changes to pitch level 35 (same as tone two) before another tone three (tone sandhi). But additionally, it is not really pronounced as 213 in connected speech anyway, but as 21 in connected speech (before other tones). Hence the functional load on the contours is somewhat lower in Mandarin than one might expect from looking at the tones in isolation.
Finally then, we have the issue of diachronic tone change. Bangkok Thai has had undergone relatively substantial changes to its citation "high" tone, where older female speakers have a "hook" in the tone such that there is a final falling section, whereas younger female speakers have a terminal rise, making the high tone concave (see this 2009 paper, specifically figure 8). That makes the "high" tone the same shape as the "rising" tone, just at a higher pitch, for the younger speakers. Older speakers are thus likely to confuse the younger speakers' "high" and "rising" tones.
Changsha Mandarin, a different branch of Mandarin from Standard Mandarin, is switching one of its 去声-derived tones (phonetic value 21) to the other (phonetic value 45) under the influence of Standard Mandarin (the tonal categories for related words are split differently). These changes in a single tone, merging with another tone, are more likely to be noticed than a simple register change across everything.
In the Fuqing dialect of Eastern Min, tone sandhi affecting both characters of a binomial sandhi domain has evolved, one of which includes a generalisation of rising tone. Fuqing is known for having no rising tones in isolation at all, but one high rising tone (35) emerging in tone sandhi. The newer generation (as of 1992!) in the Rongcheng variant (big city bit of Fuqing) has expanded the use of the sandhi rising tone to more sandhi pairs. Again, this has replaced whichever tones would have been used in sandhi by the older generation.
So, in direct answer to your question: anything could happen. But those two factors conditioning any phonological change still apply: 1) ease for the speaker; 2) ease for the listener.