I have been living in Saigon for the past 10 months. I'd say on the contrary, the first few days (what a tourist would experience) are the most stressful, but after a while you get used to it and it's alright.
Saigon and the great experience of crossing the street... among the highest rate in the world of car accidents. Come on, let's be serious, this is better than the Paris subway? Under what metric?
Vietnam isn't even in the Top 30 for traffic accidents. It isn't "among the highest rate".
Vietnam's traffic fatality rate is 26 per 100,000. About the same was America's traffic fatality rate in early 1970s before Ralph Nader convinced people to care about safety. But Americans had no problem driving on roads in 1970s. Virtually no one thought it was too dangerous to drive in America at those fatality rates.
(Today fatality rates are down ~50% from those numbers thanks to Ralph Nader.)
And the Vietnam numbers continue to decrease as the country develops. The WHO numbers are based on 2016 numbers. There were a reported 8,417 fatalities in 2016 but the WHO assumes that's a lie and adjusts upwards to 24,970 fatalities. In any case, fatalities have been dropping by about 5% a year. In 2019 there were 7,624 fatalities, for instance.
Yes everyone says Saigon. (I've lived in Saigon for 7+ years.)
In official stuff they'll say Ho Chi Minh City but in casual conversation, I'd guesstimate 80%+ of the time people say Saigon. But if someone drops in a Ho Chi Minh City instead it isn't especially noteworthy.
Saying "Saigon" doesn't have any particular connotation. Like, it doesn't mean "we refuse to accept the North won" or "we refuse to accept the renaming". (Some Viet Kieu in America are crazy about that kind of thing, though.) It is mostly just that Saigon is two syllables and Ho City Minh City is five syllables.
That said: "Saigon" tends to refer to the inner metro area. "Ho Chi Minh City" actually covers a massive area -- it is the size of a province. It is divided into 24 districts and I don't think anyone from the outer 5 rural districts would say they live in "Saigon".
Also note that the airport in Saigon still has the code SGN.