Agreed. This is an issue I've put prior thought into. My conclusion was that something like this might happen but that it would take the form of instability in the wormholes used to link time periods rather than the tech not being invented in the first place; it mightn't get off the ground or be usable for anything practical but it could exist; the different time periods would need to interact in the first place before they could destructively interact.
If a hard counter for the instability could be developed, (possibly something based on roman rings?) then interesting things would happen. If we assume self-consistency then events would conspire to prevent people from changing things: People with access to the technology would become lucky - things that they would have both the will and the means to change wouldn't happen in the first place, because that wou,d cause a contradiction. Events (in this case mostly quantum events within the particles of their own brain) would also conspire to make these people apathetic and possibly brain damaged - eroding the will and means to do something that would cause a contradiction. Finally, if they did manage to go back and try to change something they would find themselves stymied by an irresistable run of bad luck. (but if they wanted the good luck they would have to fight apathy and try to change the things that do go wrong even knowing they're going to fail because of bad luck, because the good luck consists essentially of the times where they would have tried this and succeeded.
Also, a form of cleromancy might become possible. For computer operations where it's very obvious whether a result is right or wrong (such as cracking a password for instance) you could use a non-deterministic quantum process as your input and set things so that the system will go reach back in time and interfere with itself if the result is incorrect. This would essentially constrain the non-deterministic process to only occur in the way that corrsesponds to the right answer, becajse any other outcome woukd cause a paradox
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Also, with most time travel proposals that are at least semi-rooted in real physics I'm not sure that you could go back prior to the invention of time travel anyway, rendering the question of time traveling tourists moot. I'm pretty sure a pair of temporarily displaced wormholes couldn't take you any earlier than the time that the wormhole pair was created. And as for the alcubierre drive, my understanding is that it doesn't technically move per se, so it's unclear whether the temporal effects of moving faster than light would apply to it; my understanding is that it's more along the lines of how the distance to some very distant galaxies is increasing at a rate greater than 300000000 meters per second due to the expansion of the universe
to quote futurama again, my (admittedly limited( understanding of the alcubierre metric is that it worls exactly the same as the Planet Express ship: "The engines don't move the ship at all. The ship stays where it is, and the engines move the universe around it"
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