This isn’t how bonds work
Bond prices are directly related to yields, it’s a simple mathematical relationship: cash flows are fixed, the more you pay for them, the less is your return/yield. And yields are related to prevailing interest rates on the market - this is basic economics: if rates rise why should someone buy your low yielder for the same price you paid when they can get a better bargain elsewhere now? You’ll have to lower the price to make its yield match what’s offered on the market for similar bonds, if you were to find a buyer. And vice versa, if rates fall, its higher coupon becomes more attractive and it appreciates in price.
The longer the remaining maturity, the more sensitive prices are to rates changes, as there’s just more future interest at stake. And you always have the option to hold to maturity, pocketing exactly the yield you’ve bought it at, or less if issuer defaults; and this is exactly what index funds would normally do. They only need to trade when money flows in or out of the fund or to reinvest when principal is returned.
Bond market is, like, an order of magnitude bigger than the stock market, influence will be not as big as you think, and it will actually also propagate to the interest rates due to arbitrageurs
More generally, there’s inflation risk - with bonds you’re buying fixed return in a particular currency. In 1980s US bonds paid almost 15%, which is in hindsight a very good rate, but inflation was also high. If things would get out of control and a higher or hyperinflation ensued, you’d be glad to hold on to some real assets like stocks and not worthless fiat money created out of nowhere by central banks left and right even today