Sure if one wants to play a specific type of character(s), making one as similar is OK. I recall a time when we had some players who only wanted to play a certain type of warrior or a certain type of wizard, etc, so what you ask is not unheard of.
From personal experiences, my groups had always when we started a new campaign, we used to create multiple 1st level PCs. (Because of the 1st/low level death rate.)
Each PC would be unique, as we rolled all stats.
We also used a chart for creating an outline for a background. From social status to birth order (and any siblings) to parents (profession and if they are living/dead and how) to if one's PC has a spouse and any children, etc.
So even if one wanted to create a similar character, the charts we used created enough diversity that no two were exactly alike. Their backgrounds would be different. And odds of getting similar stats (starting gold and equipment) would be low too.
So wanting to create an extremely similar character to a past character is not unheard of.
If the DM allows it, I say why not.