Why do only high-end phones support a lot of LTE bands?
Simply because having more bands not only requires a very versatile chipset, but also extensive antenna design!
To explain: It's impossible to make the perfect antenna for all frequencies, but you can make "compromise" broadband antennas. You can do that in a lot of ways, but in the end, you need to integrate those into a mobile device. And that's where it gets costly:
Now, you don't only have to simulate and measure your antenna in isolation, mounted on a low-loss mount in an anechoic chamber, but as integral part of a transceiver system (phone).
That leads to interesting solutions such as antennas being embedded in the plastic casing, a lot of time spent on tweaking the chipset's RF control registers, having multiple broadband antennas to even have a chance for diversity gain at all bands, and of course drastically increased development time and certification costs (you do have to get these approved!!).
Adding more bands to these the chipsets can receive will also add the need for more noise testing – your tuner / LO synth will have different spurs at different frequencies! So, that's another design – test – improve cycle you add for every single band you add. You can make that easier by throwing money at the problem (filters, more board layers allowing for more supply nets allowing for better isolation).
Those are all cost factors, so you don't do that if you just spin a new slightly modified phone for a specific market every two months. Or, if you really don't care for the non-{insert your home market here} market.
These high-end smartphone don't have 35 antennas. I don't think there is 35 different signal paths.
I'd agree on them not having 35 antennas. But really, the massive MIMO numbers people throw around when they're currently play the 5G-research-funding buzzword-bingo game are not that far away – mind you, not for mobile devices (physics doesn't let you have 35 statistically independent receptions in arbitrarily small receivers), and as said, you'd have to go for one wideband antenna (you can't have 35 narrowband ones close to each other and act like they are independent. Look at a Yagi antenna. There's at most one matched dipole in there. The rest is too short or too long, but still, the overall thing works as one antenna.), but yeah, having multiple active receiver chains is something we already do and will be doing more in the future.
I'd have a talk I'd like you to watch: Inside The Atheros WiFi Chipset - Adrian Chadd at Defcon14's wireless village. Not about 4G, but Wifi, but somewhere in the last third, he explains why you do not want to tune your Wifi chip to frequencies that the atheros folks didn't test, though you technically can.
Just another aspect that just hit me:
Might be the same chipset, but who tells me that Qualcomm doesn't sell you devices that have some bands disabled at a lower price than those with all bands enabled? After all, yield of semiconductors is limited by damages in all pieces of a semiconductor, not only the digital parts. Factory calibration of the chips might be a relevant production time and thus, cost element, too, so it'd be also logical to sell chips that have only been qualified on some bands at a different price than those that are qualified for all bands.