This is nonsense. I have only had my card rejected once (at a rural restaurant in deepest Provence) in the past 10 years. It has been accepted in the UK, Italy, France, Switzerland, Belgium, Netherlands, Germany, Austria, Slovakia, Poland.....
The sole exception I have found: some (but not all — it depends on the company) French toll road unmanned machines do not accept a swipe card, but then they do not accept UK Amex chip-and-pin and UK Visa debit chip-and-pin cards either. Only Visa credit will do.
Most European chip-and-pin machines have a slot down the side to swipe the card in addition to the chip-reader slot. If they do not, the operator will have a swiping slot down the side of the terminal monitor or on the terminal keyboard. All you have to do is tell them it's a swipe card. If you don't know how to say that in the local language, a gesture will do the trick. I've never had a problem, as long as a swiping slot actually exists (it didn't in Provence). Often they will look at the card, see that there is no chip, and swipe without being asked, but if I know how to say it the transaction goes more smoothly.
However, I agree that it would be highly preferable to have a chip-and-pin card.
Bizarre how much experiences vary. I spend a couple weeks each July in France during the Tour de France, so I've gotten to use (or try to use) my non-chipped card in pretty much every region of the country.
For the most part I've had little trouble in restaurants... except in Tarbes & Pau (Pyrenees) where several insisted they couldn't take a swiped card, even though there readers clearly had the slot on the side. In one case, a bakery just outside of Pau, I even had the assistance of a native who was trying to explain to the woman how to use my card with her machine. She'd have none of it. A cynical person would suggest that there are advantages to businesses to cash transactions in countries with very high tax rates.
There's also the issue that you cannot use a non-chipped card in the automated ticket machines in train & metro stations nor for unattended gas stations (commonly found on Sundays when you're trying to return your rental car with a full tank of gas).
On the other hand, I've had no trouble at all using my swiped card on tollways in any region I've visited.
Whatever the case, I'd love to have a chipped card that carries no currency conversion penalties.