I am not sure I understand what you are trying to say. Inflation either spikes up because of increased of demand, or lack of supply. In our case, both have happened:
* Increased demand because free money is hitting the bank accounts of almost everyone.
* Decreased supply because of supply chain bottlenecks, when every vendor canceled their orders in anticipation of a lack of demand (which never happened, with Covid), and then all of a sudden had to place again the same orders. Since every vendor practiced Just-In-Time order of all parts, the sudden demand (or - to put it in other words - the "lack of demand" which never happened) put them in a though spot where everyone was re-ordering the same parts again, but factories had to start with a fresh order queue.
This is not a "wealthy people problem", this is a "everyone is creating demand" problem. Wealthy people cannot create inflation in common goods because they are both outnumbered by regular folks, and because there is not too many of them anyways. How many eggs can a wealthy family purchase anyways? The demand of wealthy people is otherwise focused on goods that are not affecting the rest of the pyramid (does anybody care if yachts are price inflated because too many wealthy people buy them?).
Easy access to money caused inflation along with a supply chain bottleneck, the easy money that caused inflation was not ~2-3% loans that were accessible for 13 years prior to Covid, it was PPP loans, stimulus checks, and student loan pause, which all combined was given to pretty much the entire population of the US. Next thing you know, inflation is up.
I am not saying that people didn't deserve handouts for a very unique and though time in the history of their lives (Covid), I am just making an observation with the benefit of hindsight.
When you print money, Its unsurprising that those closest to the money printer will accumulate the most money.
In other words, had both monetary and fiscal policy stayed the same, inflation would not have happened to the extent we are dealing with right now. But fiscal policy (government handouts) was extremely liberal after Covid, and that put us out of balance.
It was a problem for a lot of people who either got priced out of the housing market or have huge student loans or have huge healthcare bills. The price of eggs or gas is really not much of a problem when the price of these big ticket items shoots up.
It may have been, but that was not reflected in the CPI, and we are talking about inflation as it is officially recorded in the CPI reports. The CPI inflation didn't spike up until early 2021.