Probably not an issue when converting between types of coin, provided you preserve value.
In short, all the parties I have every played as part of or run games for prefer to do what I jokingly call the ‘magic coin purse’ approach. In this setup, it’s assumed that platinum, gold, silver, and copper are freely interchangeable without any issues, and players inherently convert everything to either gold (what most people prefer to do when doing this), or whatever the highest value possible is (a better choice if you are tracking encumbrance from coins), and as they need lower values they just subdivide without needing to worry about it. In your example, the coins would come out instead as 3 gp and 7 sp, and a player could theoretically take 9 sp from that without issue and be left with 2 gp and 8 sp.
The only part of this that’s problematic is completely eliminating fractional gold value. This is really important, because in your example ‘conversion’ you actually lose 7 sp worth of value. That doesn’t sound like much, but when tracked over dozens of payouts it adds up to a potentially significant amount of cash.
Auto-converting appraised items to cash is an acceptable shortcut in most cases.
A lot of parties I’ve played with also do this. There are a couple of potential disadvantages though. If the items are stolen goods, and you convert like this, what do you do if local law enforcement come after you for their return after you’ve spent the gold? Additionally, that 25 gp bracelet probably weighs less than the 0.5 pounds that the gold pieces would weigh, so if you’re actively tracking encumbrance, keeping trade goods like the bracelet may be more practical than just auto-converting things to gold.
Certain gems need to be tracked independently by type.
This is important because some spells require gemstones as material components (for example, all the spells that can bring a person back from the dead eat diamonds for breakfast, and Identify needs a rather valuable pearl). In 5e, you need to do this for at least rubies, diamonds, sapphires, pearls, and possibly emeralds (depends on how your GM rules about the material components for Sequester). Some other gemstones may be required for other spells, and some spells may even require valued components that are not gemstones (I know some did in 3.5e, not certain about 5e though).
The alternative here is to hide this away as an abstraction in a similar manner to the solution for the coins and let players convert gold directly into the required material components. This approach has a nontrivial impact on gameplay, because it eliminates some need for players to plan ahead that exists under the normal rules. Whether or not that impacts your game is up to you though (I’m personally not fond of it, but I know players who have no issue with it at all).