David1961 - it's good to see an emotional attachment to things connected to your family.
However, remember that one should probably view this in an 'indirect' way, rather than a 'direct' emotional attachment, since when you get right down to it, you have absolutely no control over the item.
If you were talking about 'direct' tangible items - land, a house, a vase created by Louis XVI's personal artist - it would be completely different. However, you're talking about mutual fund shares which are entirely OUT of your control. The fund manager could really screw up and drop the fund's value...or they could even do 'average', and let their high fees eat away at the fund's value. This makes the mutual funds (IMO) an 'indirect' asset, and which should not have much emotional attachment at all.
Think about it in terms of a racing horse: what if your grandfather willed you a racing horse, except you had no control over how the horse was trained, fed, conditioned, or raced? Your father's jockey made all the decisions as to what the horse did, etc., and you couldn't even visit it to ride it around - all you had was a picture of it on your wall to look at. You are essentially in control of nothing, which could easily be neglected into an old horse, and end up being a liability. Sure, it might have some emotional attachment, but you have absolutely no control over anything related to the horse (and you can't even visit it!) - so it's almost like it might as well not even be yours.
If you want, frame the original mutual fund certificate or monthly account statement as a reminder of what your grandfather gave you to start with, and then put the money into the best opportunity you can find (for your given needs). After all, I'm sure your grandfather received some money from his father/grandfather - what if he had simply framed that money and did nothing with it? (ignoring the collectible value of old paper currency)
My point is - hard assets are one thing, but an investment like this is an entirely different situation. I'd say just have an attachment to the person and what they enabled you to START with. Don't keep the mutual funds simply because they were given to you (unless the funds are low-cost/excellent track record/etc.).
Has anyone ever been in a similar situation?
I suppose the closest thing I've been in so far was when my grandfather passed on and left my siblings and I some EE savings bonds (purchased back in the early 80s when rates were 7%-9%!). After they doubled the first time, the rate reset down to a market rate (2%-4%), so by the time we received them, it was a no-brainer to redeem them and redeploy them in higher-earning investments. That, and I was in school at the time, so my low income allowed me to pay taxes on the interest when I was in a much lower tax bracket. (Plus, with savings bonds, they stop earning interest after 30 years, so you HAVE to cash them in eventually, whether you want to or not). Thankfully, I wound up putting a good chunk of them into the new (at the time) I-bonds, which were offering 3.0%-3.6% real yields. If only I knew how good of an opportunity they were at the time!
Tangent: An interesting thing I learned (which I wish my grandfather had looked into, given how interested he was in saving on taxes) was that you can actually declare savings bond interest EACH YEAR and pay taxes on it. If I had done this in the 80s/90s growing up, I would have paid $0 in taxes then and when I cashed them in, since the interest earned every year would have been below my annual individual deduction/exemption.
So, if any of you have savings bonds that you're planning on leaving to children, look into letting them declare the interest earned each year while they're young/have low income.