They don't, due to overflow. You never lose by putting a turn on a tech you don't need. You gain by getting a higher priced tech than the expected value under randomness, which results in a net time gain irrespective of what you do with the high priced tech.
You might have had a case here pre-patch. You no longer do.
You're missing the point.
You are losing out on getting technologies (and their benefits) sooner by investing time into incomplete techs that, while still incomplete, give you nothing. When researching 3-4 techs with 1 turn, most empires can have actually completed or nearly completed a tech in the same time. What if that potential tech is useful? It probably is.
Granted, the benefits of the RAs (assuming you have enough money, willing/able suckers, etc.) can and often do out-weigh the opportunity cost, but I have a hell of a lot more than "no case" here. Also, money and ability to bankroll a RA in a time-window that allows for using this to its potential is not consistent. Also note that that kind of cash from luxury resources is only consistently available on the very highest difficulties (lower ones the AI simply won't have the chops to give you that kind of money in trade and still have money for RA) Where is the exploit?
Posit an explanation for the random mechanic that doesn't involve attempting to prevent players from executing deep beelines with Research Agreements.
I'll throw one out there:
Counter-balance to high-level AIs. With their gobs of money, AIs get to spam RA up the wazoo right from "go". Players can offset this to an extent by focusing the techs they want to get. In other words, this can be seen as a "gamey" feature left in deliberately so that high level players can compete with the AI, rather than an actual attempt at balancing player options such that multiple things are viable at high levels (something firaxis has never accomplished).
Does that sound like a reach? Maybe it should not. Bibor provides an excellent historical example that is indeed comparable to this:
Lets see if manipulating RAs has the same characteristics as beelining, say, Aesthetics in CIV4:
Randomness factor included - check.
Abusing AI teching mechanics - check.
Deliberate player action required - check.
Temporary sacrifices from player required - check.
Huge leap in player's tech pace acquired - check.
AI unlikely to perform the same feat - check.
It got to the point where on immortal/deity, you opened up with an aesthetics beeline, or in extremely good scenarios maybe alphabet or oracle. The trade ROI was just too high. But what did aesthetics itself give? Access to a couple wonders which were by and large situational, and the ability to tech literature/drama. Good, but not alpha/currency/monarch/hbr/iron working good usually. But the AI ALWAYS went for those, and the player could therefore almost always get all of them by researching...aesthetics. The liberalism bulb beeline as another more advanced example of this as well.
So what did the designers do?
- Make the AI not value the tech as highly? No
- Make the AI tech it more frequently? No
- Change the value of the tech or the pre/post reqs? No
- Do ANYTHING to change this tactic? No
They left it in, and left the AI with bonuses that forced the player into it. Unless they're cooking something beyond BTS 3.19 in secret, that is ther permanent position.
How about apostolic palace?
- Did they ever, EVER make it so that the religion needed to be relatively popular? No
- Did they even make it so that you had to be running the AP religion to win AP? No
- Did they stop the spreading of the religion to civs in theo, by simply gifting the AI the missionary so that the AI would spread it w/o exception? No, even though unofficial patches did that.
- Did they do ANYTHING to stop players from cheesing the AI on deity so badly that it was possible to win with a 20000 beaker hole and only 1 AI voting for you? Absolutely not.
I can go on with examples, but the reality here is that firaxis has a LONG TREND of leaving holes in their games and then "balancing" it with herp derp bonuses, locking player tactics. Then you get droves of rookie players who cry over high level strategies that are essentially forced because OBJECTIVELY, no civilization game has ever balanced its options or victory conditions. No civilization game has even come close. Whether people care or not is another issue and for this thread, irrelevant. Firaxis history on this matter is QUITE clear.
So there's one possible explanation for you.
An alternative explanation is that in each case, firaxis was incompetent in balancing the features and thus left overpowering options/holes in its games. However, if you go that route you can quickly follow that explanation to a logical conclusion that the games aren't finished, are imbalanced, and the total lack of balance merits breaking "designer intention" because the designers had no intention of releasing a complete product. That view, while a lot more cynical (and probably more realistic), does not help the "exploit" side of the argument, however. In a mess of a game where "ranged attack" = "move sideways" sometimes and victory conditions don't even pretend to be balanced, calling tactics out based on being exploitative misses the big picture. So don't try it

.