As somebody else has mentioned, The Suzuki Swift does have a spare tire, only the Suzuki Swift sport is without. (and I imagine the 4wd swifts out of japan).

Not having a spare tire is becoming quite common. No BMW comes with a spare tire, and only some of the BMW SUV's have them as options. they have run-flats on some models, and normal tires on others). Spare tires are rare on electric cars, and on sports cars.

This is not such a big deal. Unless you do a heap of course gravel driving, flats in modern tires are rare. Also many modern cars have tire pressure sensors that will indicate a tire leak well before the is flat.

A lot of research in the USA indicates that a relatively small number of drivers know how to change a wheel, and of those who do know, a decent chunk of them would call a roadside assistance service rather there tire at the side of the highway. (Excludeds pick up trucks, and off road type 4x4's)

Auto manufactures are taking advantage of this knowledge to scrap the spare tire, saving $150 odd from the manufacturing cost of the car, and offering bigger boot space, and releasing the performance / eco advantages of 30kg of weight savings.

Big rig trucks rarely carry spare tires anymore (the wheels / tires (typically multiple sizes per truck), combined with equipment to fit them (jacks etc) is expensive an heavy). Every KG of spares you carry is 1 kg less of payload you can sell... It is more cost effective for them to have the driver wait for a tire service, than carrying spares.

For your situation I recommend:

• Replace your tires at 3mm tread depth rather than the legal min of 1.5mm. This will massively decrease the odd of a puncture. (also, wet drip starts to drop away below 3mm of tread depth so it is also good for safety and wet performance).
• Check your fix a flat can new/full, and includes a 12V compressor. (If not I would buy a cheap compressor one and carry it. This allows you to air your tire up to get home without putting the goo in it - something that will likely write of the tire and Tire pressure sensor if any).
• Check and see if you have flat tire detection (will be in your manual, likely the flat tire symbol will flash on and off each time your start the car). As others have said, can be added aftermarket if it gives you peace of mind. These are required by law in the USA for safety reasons. Basically without them it is really hard to tell if you have an under-inflated rear tire, continuing to drive on it can lead to the sidewall overheating, and blowing out, creating a dangerous handling situation.
• Take your phone with you when you are out in the car.

The above should provide enough piece of mind. I didn't have any worries when I had the i3 (which has no spare, no runflats, just a compresses / goo kit).

Probably should avoid ultra low profile tires too as they are more prone to road damage.