First off: One should not make the mistake and equate ancient languages with today's. There is an important difference between having a) the bigger half of the population live in remote areas with changing rulers every full moon, with a tremendous analphabetic rate; and b) having a reporter every evening read the prestige dialect or standard form over the air in a stable country. Anyhow, remote areas still exist, so comparison in situ is surely done.
The struggle for a unified language is very real today for Serbo-Croation for example--or not, depending on which side of the fence you sit on. However, from a historic perspective, for the most part, the winner will leave the majority contribution to the imprint of the language.
The truth is, that language consists of idiolects per person that can change somewhat over time. That's of course beyond impossible to work with, though dialect research is a thing, of course, so researchers necessarily have to simplify. This is not quite so bad under the assumption that a native speaker will operate from a rather inert core--that's why L2 accquisition is so diffficult passed a young age (and that's why writing has to simplify. Therefore the trunk of a languages development is supposed to be reconstructable quite easily, even if taking stats for only one semester just barely passing. The branches, fruits and everything else is rather difficult;
The discovery of a common Indo European family is barely two centuries old. The field always adds disclaimers, for good reasons. It's work in progress, few people have the prowess to engage, little is certain. Traditional etymology is littered with false etymologies that have become part of the language and need to be separated, religious or nationalistic nutters are trying to contribute, scientific rigor and interconnected exchange are kind of a new thing, too. The biggest showstopper is always the homeland questions, that requires experties outside of the field, and evidence that is burried or lost. That means, I fully agree with the sentiment of the question.
In order to understand the reconstructions, one has to learn them like any language, that makes it feel very real. However, there is no one proto language; The ideas differ like idiolects do, except for a common core. The core words of an idiolect, like most any words as well as the reconstructions are symbolic. If concensus emerges from the words, then they have become defined. For a research language, that means these words reflect sensible relations. We can call that a language, because the concensus on the definition of a language is rather weak! Just ask a linguist what a word is and you will get many opinions.
The assumption that there was at least one cohesive language is simply necessary. There can't have been zero, after all. Whether there were more is an interesting question, and slight differences at common joints may be worthwhile to consider. However, potato, potatoe, is just seen as an aspect of realization. Alternative spellings, if one can call it that, are given due to different results. Focusing on just one restrictive theory can be a real problem, but it's also the goal. That's the real problem.
Language needs to be locally and temporally bound, thus a working theory needs to try to stay within the bounds. Nobody makes strongly specific claims to the extent of the boundaries. In mathematical topology, disjoint areas can still be treated as a unique set. In that sense, the boundaries could be quite complex. Nobody is really talking about a single point, it's just an abstraction.
Graded dialect continuums are not unheared of in the field (e.g. for PIE in Gramkrelidze & Ivanov; I have no idea about Slavic specifically). The possibillity of Substrate Languages has caused various speculations, too.
