Farewell Millemiglia, which program to target for the next award tickets?
The reward travel strategy involves accumulating points and miles to be later turned into award tickets and free stays. [...]

The reward travel strategy involves accumulating points and miles to be later turned into award tickets and free stays. The end, inglorious, of the Millemiglia program. and the announced emergence of a new ITA company loyalty program, or whatever it will be called in a few months, do not bode well for Italian serial accumulators.
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The reason is simple, if even ITA would present the perfect loyalty program tomorrow morning, all would come up against the bitter reality of a provincial airline fleet and an unattractive network of destinations. Once the alliance with which it will start again is defined between Skyteam, Star Alliance, or One World, the only real driver that could change the scenario could be to have a very aggressive award chart.
We have seen, especially in the U.S. market, strategies of this kind, for example with Alaska Airlines and other airlines that in order to attract frequent flyers and also indirectly advertise themselves have offered very attractive, almost below-cost "price lists" for award flights.
Without this situation, aiming for the next 24/36 months to accumulate points in ITA's new frequent flyer program could be a blind bet given that routes for summer 2022 will be few and far between and always the same.
Beyond 2022 everything will depend on market, account and fleet performance. A wait that could end in a Yet another hole in the water with yet another failure And dispersion of accumulated points.
How to accumulate points in Italy from other loyalty programs
Personally, in the coming months for the Italian market I expect a lot of news, especially aggressive policies by European companies interested in the Italian market in light of ITA's obvious weaknesses. We have already talked about how so many have jumped on the traffic to/from the United States, I imagine the same may happen to convince MM orphaned users to switch to other programs such as Lufthansa Group's Miles & More, AF/KLM's Flying Blue, and I would not underestimate Iberia and British's Avios points.
Of course, the choice must be made primarily on the basis of the destination you will want to reach and taking into account point deadlines and possible sudden devaluations of premium tables.
Why choose AVIOS
The most obvious thing from ITA's new operating is that it will not fly to South America until, at least, spring 2022. Easy to foresee, then, that Iberia may offer aggressive fares to leverage its network to Latin American countries, which are historically a very important market for Italian passengers, both leasure and biz.
Avios points also have the advantage of already being present in the Italian market through many partnerships. The advantage of being able to move points indifferently to Iberia and British Airways also allows them to manage the eventual award ticket across the entire One World network, as well as take advantage of a very attractive award table that allows Fly to the U.S. in biz starting at just 34k Avios. Last but not least, it currently has the best conversion rate among all the American Express partner programs.
Why choose Mile & More

Lufthansa's business class on the 747/800
Currently in the Italian market there are. Two credit cards, issued by the Unicredit group, which allow people to accumulate points in the German carrier's group loyalty program. This is certainly an important advantage for those using this accumulation strategy. Of course, it is not an avenue open to everyone since the issuance of the cards requires having a current account with the Milanese bank, also because none of the other loyalty programs in Italy have this option. At least at the moment. Note also that not being an Amex partner, it is not possible to turn MR points into M&M program points.
Why choose Flying Blue
Air France and KLM fly virtually everywhere, also being deeply connected with Delta and Virgin Atlantic allow you to really choose from so many destinations and with some of the best products in the world such as Premiere, or the first class of AF., or Virgin Atlantic's Upper Class. However, there are no major partners in the Italian market, excluding of course American Express and Membership Rewards points and at a significantly less affordable rate than Avios.
All other programs
I don't see many other choices on the horizon, because it is impossible to accumulate so many points in an alternative way to flying with programs like Tap Portugal's or other airlines that fly to Italy and could be interesting for a reward travel strategy in our country.
Perhaps a separate discussion deserves Emirates. Of course, accumulating points with this company in an alternative way to flying is difficult, but thanks to the flight to New York and to network to the whole world by flying via Dubai it might be smart to accumulate Membership Rewards points starting with American Express Gold, for example. and then turn them into points Skywards perhaps also taking advantage of the Skywards+ offer. which allows you to get an important milesback which is very reminiscent of the old American Express Alitalia green card.