What would be the most challenging aspect to modernize a 2-stroke engine?

The most highlighted 2-stroke gasoline-powered car engines in Brazil were fitted to the DKW-Vemag range, made under a license from the same Auto Union which would later be reorganized as the modern iteration of Audi, with the brand changing from DKW to Audi reflecting exactly a switch from ancient 2-stroke to 4-stroke engines which were perceived as state-of-the-art in mid to late-'60s. Littie could'be been tried in order to make the DKW 3-cylinder 2-stroke 1.0L engine better suited to a more prestigious aspiration such as in the DKW-Vemag Fissore, even though the Lubrimat system resorting to a separate oil reservoir instead of requiring a fuel and oil premix noticeably decreased both smoke and spark-plug fouling under certain engine loads, and could be effectively more practical than having to change the oil in a 4-stroke engine periodically, even though the total-loss oiling would not be much suitable to forced induction through a turbocharger, and even if a belt-driven supercharger could be implemented it would need its separate splash-lube oil system. Back in a day when electronic fuel injection sounded more like sci-fi, and mechanical fuel injection was much easier to justify for Diesel engines due to a much higher complexity compared to carburettors, the fate of 2-stroke engines in cars was sealed...

Besides the automatic lubricating system through oil injection, which would later also become popular in 2-stroke motorcycles, other developments started to emerge in the '70s when an "outdated" 2-stroke car was turned more into a technical curiosity in Western countries and more efforts were directed to the evolution of 4-stroke engines. Just like intake reed-valves and exhaust power-valve systems which were fitted to some 2-stroke motorcycles eventually provides an effect comparable to what a 4-stroke engine would get with a variable valve timing, it's worth to notice the differences between the intake flows in a 2-stroke engine posed additional challenges for electronic fuel injections to become effective regarding fuel economy, with both direct injection at some earlier stages and more recently transfer-port injection being implemented to certain 2-stroke motorcycles, all while the economics of scale are more difficult than a port-injection setup in a 4-stroke. So, besides cost and economics of scale favoring 4-strokes, an increased hardship to adjust either a direct injection or a transfer-port injection to inject a fuel in liquid phase such as gasoline or ethanol as well as certain alternate fuels such as CNG or Hydrogen in vapour phase might have become the most challenging aspect for any attempt to rehab 2-stroke engines in cars.

The Fiat Pulse makes downsizing seem rather pointless

One of those Fiats developed more specifically to the Brazilian market, the Pulse was released with the GSE/Firefly engine, always in flexfuel trim for Brazil and gasoline-powered for regional export, with a 4-cyl naturally-aspirated 1.3L version as the entry-level engine (and only one available in Mexico) with either a 5-speed manual transmission or a CVT automatic and the 3-cyl turbocharged 1.0L MultiAir III only with a CVT. Later a sporty Abarth trim with a MultiAir III version of the 4-cyl 1.3L was added, with a more conventional 6-speed automatic, but the rather specific profile of a sporty model might not be so unjustifiable for turbocharging. However, for the regular trims, the naturally-aspirated 1.3L ended up with a better fuel-efficiency, even though the 1.0L turbocharged was supposed to be much better and technically superior, with its direct injection rendering unnecessary as a knock-suppression measure an excessive enrichment of the air-fuel ratio under boost which used to be more usual when port-injection was the rule even for turbocharged engines. Sure the 56.25% higher torque rating for the 1.0L MultiAir III might be appealing, not to mention the turbocharged provides some altitude compensation once the turbo-lag is over while the naturally-aspirated engines suffer from a more acute performance decrease on extreme altitudes, and considering FIA racing homologation rules the turbocharged engine with a 25% lower displacement would actually be supposed to equate to a naturally-aspirated engine 27.6% larger in displacement than the one fitted to the Pulse, which technically is quite impressive, but the turbocharged engine ends up not only having a higher fuel consumption but also costs more to make and mantain. It's also worth to notice that some operators such as taxi drivers may also consider to upfit the vehicles with a Compressed Natural Gas alternate fuel setup, to which the port-injection of the 1.3L naturally-aspirated engine is still better suited.