You can understand why: the bridge between Europe and Asia; bridges across the Bosphorus; or, as bid chairman Hasan Arat, put it on Saturday (June 15) in the Olympic capital of Lausanne at the Extraordinary General Assembly of the Association of National Olympic Committees (ANOC): "Istanbul offers the Olympic Movement a bridge to a new culture; to a region and a people who have never hosted the Olympic Games before."
A potential problem for the bid, though, is that Turkey has also been seen, I suspect, by some in the Movement as a bridge to the Gulf - or more prosaically, as a majority-Muslim alternative that could forestall for another few Olympiads the steadily mounting pressure for the Games to go to the Gulf.
This means that when something goes wrong, like Taksim Square and the torrent of unfavourable international media coverage the handling of the protests there has provoked, there may be a greater tendency for that support to melt away than backing based on the specific - very manifest - qualities of Istanbul as an Olympic host and the merits of its Games plan.
With nearly three months to go before the crucial vote in Buenos Aires, I don't think the situation is yet terminal for this imaginative bid with its promise of an amphitheatre for the Games every bit as spectacular as that offered by Rio de Janeiro, the next Summer Games host.
Any bid winner requires a coalition of different brands of support.
Moreover, as has been observed elsewhere, the International Olympic Committee (IOC) is very much a fan of strong political leadership.
As I write, there may still be enough room for manoeuvre - just - to enable Prime Minister Recep Tayyip Erdoğan to emerge with authority shaken but not undermined while placating some of the protesters and enabling bid leaders to laud a mature, tolerant, secular democracy, as National Olympic Committee of Turkey President Uğur Erdener tried to do in Lausanne.
That said, I saw it reported that the protests had achieved the difficult feat of uniting - bridging together? - supporters of the city's three rival football clubs, suggesting that grievances are widely shared.
As my friend, the eminent football writer Simon Kuper Tweeted, alluding also to Egypt, "Wish I could rewrite Football Against the Enemy".
So who stands to be the main beneficiary of Istanbul's present discomfort?
My first inclination would be to say Tokyo, whose bid has achieved a lot more traction than last time around, when it finished third in the 2016 race.
But, actually, it may also have let Madrid back into the game.
Alejandro Blanco, the Spanish capital's bid leader, has said that Spain's new anti-doping law will add to the bid's credibility.
I would say it was indispensable if Madrid 2020 were not to be dead in the water.
Nonetheless, having bid now on three consecutive occasions, the West European candidate can legitimately claim credit for its persistence - just like the 2018 Winter Games winner, Pyeongchang.
And London 2012's success may work in favour of the tried and trusted over the adventurous and new - particularly in light of rumblings over Rio 2016's progress and the still delicate state of the global economy.
The Spanish city also tends to perform strongly in the first round of voting, although it is campaigning this time without the inimitable presence of Juan Antonio Samaranch senior, the late former IOC President.
If it can supplement its core vote with some latecomers, switching from the Istanbul camp, then we could once again have a surprise first-round casualty at the vote in Buenos Aires.
I must say I also slightly fear for the impact that the simultaneous race for the IOC Presidency might have on the Turkish bid's chances.
I sense an incipient dilution in the apparent antipathy I have often felt in Olympic circles for the notion of hosting a Summer Games in the Gulf.
This may, in part, be a by-product of the courting of IOC members from the Gulf region - who include Kuwait's increasingly influential Sheikh Ahmad Al-Fahad Al-Sabah, the ANOC President - by candidates for the top job.
But I would be surprised if the new IOC leadership did not appear less hesitant than the present incumbents about the whole idea of a Gulf Olympics, perhaps as soon as 2024.
And if a Gulf Games is becoming a more attractive prospect, then why would you need to forestall it by voting for Istanbul?
The sheer number of high-level decisions that IOC members are being required to take in quick succession makes calling the outcome of any particular race more than usually hazardous.
But it is hard to concoct any "spin" under which this has been a good month for Istanbul 2020.
David Owen worked for 20 years for the Financial Times in the United States, Canada, France and the UK. He ended his FT career as sports editor after the 2006 World Cup and is now freelancing, including covering the 2008 Beijing Olympics, the 2010 World Cup and London 2012. Owen's Twitter feed can be accessed here.