Zakat is money paid on "wealth". So if someone has a certain wealth for one lunar year then zakaat is applicable on it provided they cross nisaab.
Let’s say you collect for something expensive like a car or education, 2.5% is not a very big amount in the beginning to mid of the collection period, but towards the end it would get a little difficult and you would reach your target of collection a few years late.
Technically speaking not paying zakaat and collecting wealth may be even considered hoarding...which is forbidden
[9:34] "O you who have believed, indeed many of the scholars and the monks devour the wealth of people unjustly and avert [them] from the
way of Allah. And those who hoard gold and silver and spend it not in
the way of Allah - give them tidings of a painful punishment."
Also, based on the verse below, I recommend that people be safe and pay the zakaat rather than have to answer for it in the hereafter.
[41:7] "Who do not give the obligatory charity (Zakat), and with regard to the Hereafter, they are disbelievers."
PS: A personal advice I'd give people especially for material things like cars and homes, is to live within means. If a car or house takes years to collect (since we cannot take on interest), then it is probably not within our reach and we should may be dream about something smaller.
From the Sunnah, if you see when the Prophet (pbuh) passed away, his house didn't have oil for the lamp. Keep in mind that he was the undisputed leader of Arabia then.