That is a very good question. On this Sienna, it's in good enough condition that I'd probably bite the bullet and do it. With the Odyssey, we had the choice of doing it or walking away, and since the Odyssey didn't meet our needs anymore, we chose to walk away. Well I managed to get $250 for it. lol. I'll update the final cost of owning that vehicle later.
$2900 is about 5 or 6 lease payments on a new minivan. Because it's so clean and drives like a new minivan, I'll take that analogy and say after 6 months, it doesn't owe me anything. If the transmission goes, and that's a big if, I would say I could have a good used transmission installed with a one year warranty for about $1800, that's three and a half lease payments. I did have that option for my Odyssey at one point but that ship sailed very quickly with no other options. Good used Sienna transmissions however seem to be more widely available because frankly, they don't fail.
Obviously I want my Sienna to cost way less than lease payments. And when I look at the Truedelta stats on used Siennas, I think the odds are in my favour. 65 vehicles per 100 per year needed repairs beyond routine maintenance. 23% of those trips were engine or transmission related, 82% of those repairs cost less than $999, 16% cost $1,000 to 2,499, and 2% cost more than $2,500. Then 22% of the repairs were brakes and suspension related, 35% electrical and A/C related, and 21% miscellaneous others. Overall, repairs that cost more than $2,500 account for 1% of all repairs, $1,000 to $2,499 14%, then 85% are under $999. Looking at those stats, I can expect to put about $2,425 in repairs above and beyond routine maintenance over the next 5 years. Obviously a single $2,500+ repair will blow that away but there's about a 4% chance total over five years of that happening. My Odyssey's expected 5 year repair costs were about $2,590 but there was a whopping 20% chance over five years of a major repair over $2,500 happening, which would've happened if I opted to put in a re-manufactured engine at a cost of $3,500.
TL/DR: My Sienna should provide years of reliable low cost service.