I'd gladly belong to Nintendo UK or Germany, if it means being able to collect coins and get awsome deals...

Yep Nintendo is super desperate to sell their games. That's why Luigi's Mansion 2 is going for 56€ instead of 40€ on amazon.de. Nobody wants it.

Edit: I wonder if I can register Luigi's Mansion twice and be eligible for the promotion since I have two registration codes.

Or, you look at a couple of different factors, mainly the ever increasing digital success of 3DS in Japan and North America, and the absence of any such good news from Europe, which suggests Nintendo need to do more drive up the use of eShop in Europe. You can see evidence that this is part of a larger strategy on Nintendo of Europe's part, and not some panic mode giveaway.

1) The promotion you have mentioned. By giving a free digital game to new 3DS owners last Christmas, Nintendo familiarise new 3DS owners with their eShop and the convenience of digital games from day one.

2) This current promotion. By using the higher profile, higher quality releases, and by specifying 3 releases in a short period, Nintendo pitches this offer to their most dedicated and most profitable fans. Again, this helps to familiarise their fans with the convenience of digital purchases. Importantly, it also allows users taking advantage of this offer to purchase an additional title--I'm sure many fans will now download a free game, and use that money on another 3DS game. Nintendo themselves will also taken this into account.

3) The recent iDEAME sale of indie titles on Europe's eShop, to celebrate Nintendo's iDEAME conference in Spain. Not only does this sale encourage greater sales of download only software, it pushes forward Nintendo's ever developing relationship with smaller developers, increasing the chances of a great array of content on eShop in future, which, by extension, makes the eShop more attractive to a wider variety of consumers in future. Level 5 titles are also now discounted temporarily.

4) The half-price sale of Ocarina of Time 3D on eShop for one month. Nintendo have followed this up by releasing older titles on eShop at a reduced price--competitive even when placed against comparative retail prices. This helps to address one of the most basic problems the European eShop faces: digital titles available at retail have invariably been available more cheaply at retail, and a lack of flexibility in digital pricing.

It's pretty clear this is part of a concerted strategy by Nintendo to improve their digital business in Europe. It's not a knee jerk panic reaction, nor is it a sign that the 3DS doing extremely poorly in Europe. Rather, it's a sign that the digital transition underway in North America, Europe and Japan--a digital transition vital to the future of every games console, not just 3DS--needs more effort before it gains traction on 3DS in Europe. This isn't surprising. Nintendo's business has been slow to move towards digital content, preferring retail and physical copies, and online uptake on Nintendo platforms has always been lower in Europe than North America or Japan, and this is equally true for 3DS. It is only natural in this case, that more needs to be done to boost digital awareness and use in Europe for 3DS.

I'd also like to point out that the average attach rate of handhelds is historically very low--often no higher than 3 or 4 pieces of software per hardware unit. Selling three games and offering a fourth free over a three month period is therefore not naturally indicative of very slow software sales, as you assume. Finally, Monster Hunter, Luigi's Mansion 2 and most recently Fire Emblem have debuted in the top 10 or top 5 charts in many European countries in recent weeks. It's less about overall software sales, and much more about increasing the digital proportion of software sales.

EDIT: Added links for sources. Edited again with more links for more sources.

It's just that giveways of such recent releases are not commonplace. I sense some panic mode here imho. Such plan implies that they don't expect the average 3DS owner to buy more than 2 games in that period (hence they offer a 4th one at 3 purchases) : this must be behind their objectives. And last Xmas in France they were giving a free digital copy of Professor Layton 5 for every purchase of the system. Such agressive marketing clearly suggest they're in a though spot with 3DS in the West.

OT but there's also a new 3DS XL color coming to Europe (31.05.):

BTW: Thanks for the tasty doooooom.