First, it's fossil fuel that has a marketing issue. First of all, you have to pretend the second hand value of your car is not going to rapidly tank as EVs take over. If you are buying Diesel, I hope you factor in that it will be a hard sell in a few years and you might have to write off a lot more than you bargained for when you sell at a much lower price than you hoped. IMHO Diesel is the canary in the coal mine here; the same will happen to petrol cars in a few years. This will rapidly kill the market for new ICE vehicles as there is no point in buying them if you can't pass them on at a reasonable price a few years later.
Secondly, fossil fuel cars benefit from all sorts of government protection including tax benefits for big oil, tax funded expensive wars in the middle east (at trillions $ cost), silly subsidies for things like bio diesel, etc. And that's before you factor in the damage burning fuel does. Which people seem to be allowed to get away with for absolutely free. If you stop all that overnight, ICE based cars would become a really hard sell because fuel prices would rise, and manufacturers would be retrofitting cars with expensive fixes to make them stop being a health and safety risk in fear of action law suits. Think tobacco industry here. Why not? Diesel/petrol, fumes kill people, by the millions with long term health affects and measurable life time decreases. There's no good reason for any of this to continue to be the case as EVs become widely available commodity products available at competitive prices. This is more than a little marketing challenge as governments world wide seem to be cracking down on this with taxes, vehicle restrictions, etc. And that's of course aside from the whole co2 business. I know, not a popular topic but it's having real effects on fuel prices and vehicle taxes in most civilized places at this point. I don't see that ending any time soon; rather the opposite.
Norway is leading here, but plenty more countries are following. This will kill demand and increase cost for ICE based vehicles. That's why GM and Ford shut down a lot of their ICE business last year and why the likes of VW are making tens of billions of investments in production capacity for EVs over the next few years. In fact, most major manufacturers are effectively divesting their ICE business for a few years now. A few percent now, doubling every 18 months or so creates a nice exponential growth curve for EVs. Meanwhile, everything else is dealing with shrinking markets, declining ASPs, increasing taxes, government pressure, etc. There's very little future in ICE based vehicles, judging from how major manufacturers are behaving in the last year.
Charging infrastructure is just fine. There's plenty of it already and more is on the way. Actually, most of it is under-utilised most of the time (<10%). So, there's plenty of room for growth short term and plenty more long term as there are continued investments in charging infrastructure happening everywhere. Sure, in the utterly unrealistic scenario that everyone would switch overnight to EVs this would indeed be a minor challenge for grid providers. But growth as per even the most optimistic scenarios, provides plenty of room for continued investments in infrastructure, clean energy, etc. You say problem, I say business opportunity. Most healthy businesses would consider predicted growth spread over multiple years/decades to be fantastic news. Of course it kind of sucks if all you know is burning coal/gas and all the cool new hip kids are undercutting your prices with solar/wind.
Battery life is not really a problem for the vast majority of commuters. Even with the unimpressive/limited range of already obsolete first generation vehicles like the Nissan Leaf or Chevy Bolt. Long distance travel indeed requires annoyingly long charging breaks; but on the other hand taking a break after 200-300 miles is not the end of the world. And if you drive those kind of distances daily, your life sucks much more than that of most drivers stuck in perpetual traffic jams. Luckily, faster charging high end vehicles with longer ranges are becoming available as well. And that's before you factor in battery R&D over the next few decades that will decimate cost and double/triple capacities.
But most people rarely need to rely on public charging points since their car will be fully charged when they unplug it at home in the morning. And coming back to the charging infrastructure, most people see a measurable but not spectacular increase in their electricity use while charging almost exclusively at home. You have to drive a lot to double your usage. So if that's the same for most people, we're talking probably much less than 2 x increase in total electricity demand. And that's spread out over the next 10-20 years. Also, charging happens mostly off peak at night. And you can do some interesting things such as use charged cars to provide power back to the grid during peak hours. In short, this is not an issue now and unlikely to become one.
Finally, battery life span seems awesome in first generation vehicles. Mostly their batteries get reused rather than recycled after their vehicles are written off. Tesla guarantees 100K+ miles for their drivetrains + batteries at or above 70% capacity: reason: they know full well, they can do at least double that. I think Elon Musk was actually boasting numbers closer to 500K miles recently. Most ICE cars would go to many expensive maintenance cycles every few tens of thousands of miles.