The few thousand dollars you might save not buying a TV or cell phone isn't going to do shit to get you out of poverty. You can't save your way out of being poor a nickle and dime at a time.
It means you can stop wasting money on buying necessities constantly in small quantities, not pay massive interest on credit cards or payday loans because your needs a sudden repair, etc. Will this solve the problem? Surely not for everybody. But a big problem (even if far from the only problem) with getting out of poverty is that it's a trap because it's so expensive to be poor.
Except it doesn't mean that. It means that when you have $300 in the bank instead of buying a cheap TV set, and suddenly your car needs $500 in repairs, you're still going to a payday loan place, except you're on the hook for $200 instead of $500. Still paying the fees, still stuck in the let's-rip-off-the-poor cycle, except you also don't have a tv set.
I know, I know, now you'll say "well you're poor, what do you need a tv set for, you should sit in your dank apartment with just the road noise for entertainment," and that's where the compassion kicks in: these folks are poor, they're not animals, and if TV lets them be less miserable, it's about as cheap a way to do so as is reasonable.
Are you saying that being on the hook for 60% less in interest and fees isn't an improvement? Is a millionaire still stuck in a poverty trap because it's theoretically possible for them to get hit with costs that exceed their savings? What you're describing sounds like a huge improvement, not "still stuck."
Regarding your second paragraph, no, I wouldn't say that. I'm not actually passing any judgment here. I don't think that buying iPhones and fancy TVs is a particularly wise choice for poor people, but I also don't really fault them for it. I'm merely giving an example of something which could help with poverty but which the government can't provide. A decent chunk of poverty comes from poor financial choices, and that's just an observation without implying any judgment towards the affected people.
Except that sitting all day watching TV is CERTAIN to keep them on welfare for the rest of their lives.
Perhaps buying them books instead would work better?
Community colleges are very inexpensive, there are state grants available to the poor. Why not create incentives to learn a skill/trade, perhaps a degree?
"Give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime"
It's 'poor people have refrigerators' in another guise. It is apparently a laudable goal to decay our social infrastructure till large parts of our cities will resemble African poverty.
TV's are completely different to fridges in this discussion, I'd say. One is pure entertainment, the other has functional uses that help reduce costs, as well as improve health by preventing food from going off.
That's practically irrelevant, and also stunningly blind to how humans actually function. Entertainment is important - its sufficiently important that we've dedicated considerable resources to it throughout the sum of human history, to the point that we ship giant entertainment venues to warzones.
But more to economic point: TVs are cheap. The TVs people complain about are maybe ~$500, and you can do very well if you shop second hand. They are a one-off capital expense which considerably improves your life, and which the lack of sale thereof utterly fails to meaningfully help you not be poor.
Because poverty is a flow problem, and it fails to be defined by whether or not one owns certain conspicuous goods. If we were talking about impoverished people who were nonetheless buying $3000 LCDs on debt every few years, then we might have something to talk about. But since concrete examples are always conspicuously absent when points of this nature are brought up, I'm content to point to the economics: selling your TV wouldn't meaningfully improve your situation, buying a TV doesn't meaningfully degrade it.
It's also worth noting that in a discussion of being unable to climb out of poverty, requiring people to dispose of all their worldly possessions before we help them is a good way to create a poverty trap.
You are missing the point of welfare: it is supposed to help people get back on their feet, not keep them dependent on taxpayer's money for the rest of their lives. So training/education, not TVs and computer games.
That $500 could perhaps buy supplies to study at a local community college (tuition waivers/scholarships are available).