I was watching my daughter taking her first film photo's this week-end, armed with my old 'Brick', an ancient Zenith 35mm SLR.... that is one heavy camera. I'd forgotten just HOW heavy it was, TBH. And when she stopped to take a snap? Well after getting the meter out and waving it around a bit, twiddling dials, asking me if she had the ASA slide in the right place, then going back and fiddling with the shutter speed and peeking at the hyperfocus scale and re-checking aperture.... she was having to make a new meter reading, as the nice evening landscape had become a sunset

... no not quite that bad... but when she was ready to press the button..... it was interesting watching some-one else use my equipment, and as she released the shutter, the clunk and wobble of the mirror mechanism going up.... even damped by all the mass of that brick-like camera! It was like watching the recoil on a pistol being fired!
But that is the sort of load and vibration that a 'good' tripod is designed to support and damp.
In years past, my Silk tripod used to live in the boot of my car along with my walkng boots... and in fact my M42 Fit camera; 'just in case'.... and hiking up the Penines; Snowdonian valleys, or Iron-Age hill-forts in the Vale of Evesham..... You know, I never saw a FAT photographer at the top of the hill
But, in years on, a certain ecconomy of effort was achieved... sort of followed this logic.....
I'd look up the hill, and think "There must be a fantastic view from up there" Then I would look around and see a neighbouring hil, maybe five miles awayl, and think "And over there".... then look at the tripod and gadget bag, and think hard about what I REALLY needed to lug all the way up..... Nope, dont need a bag full of prime glass.... certainly don't need the long lenses, maybe the 28 and the 50..... then after a few excursions lugging to the top of hills with loose lenses in my pocket and camera slapping on my chest..... further ecconomy of effort was found JUST taking the 35mm compact to the top!
And I'm looking through strips and strips of old negatives as I scan them now, and honestly.... so many landscapes I cant really tell whether I took them with fancy SLR and 28-70 or my little fixed lens compact!
Meanwhile.... using smaller lighter camera.... perching iddy-biddy little compact on top of big sturdy pro-tripod, seemed so..... rediculouse.
I got a little mini-pod. Pocket thing about the length of a biro! It's FANTASTIC!
Wont take the weight of that old Zenith, I have to say; but did prop up the compact well enough, and I have stuck modern DSLR on it.... its probably a tad big for it, but it holds it up and if you tighten the head up, steady 'enough'.
May mean laying down between sheep-droppings to see through the view-finder from time to time, but usually you can find 'something' to put it on top of, if you don't want it on the floor.... rock, tree-stump, stone wall, fence post, car roof. Imagination & a little improvisation.... what photography is all about isn't it?
So..... yes and no is the answer to the question.
No I don't always carry my 'big' tripod, but yes, I almost always carry a little one! Even with the compact, just slips in the empty camera slip with a spare set of batteries and an SD card.